Current Electricity - Chapter OutlineLesson 1: Electric CurrentWhat is an Electric Circuit? Requirements of a Circuit Electric Current Lesson 2: Electrical ResistanceJourney of a Typical Electron Resistance Lesson 3: Ohm’s LawOhm's Law Lesson 4: Electrical PowerPower: Putting Charges to Work Common Misconceptions Regarding Electric Circuits Lesson 3: Circuit ConnectionsCircuit Symbols and Circuit Diagrams Two Types of Connections Series Circuits Parallel Circuits

Lesson 1: Electric Current - objectives

1. What is an Electric Circuit? 2. Requirements of a Circuit 3. Electric Current 4. Power: Putting Charges to Work 5. Common

Misconceptions Regarding Electric Circuits

What is an Electric Circuit?

A circuit is simply a closed loop through which charges can continuously move.

lab: light a light bulb• you are given the following material, what arrangement

would result in the successful lighting of the bulb?

• Record all different ways your connection did not work.• Record all different ways your connection did work. • Write your conclusion – what you must do in order for the

light bulb to work.

Light Bulb Anatomy • A light bulb is a device consisting of a

filament attached to two wires. The wires and the filament are conducting materials which allow charge to flow through them. One wire is connected to the ribbed sides of the light bulbs. The other wire is connected to the bottom base of the light bulb. The ribbed edge and the bottom base are separated by an insulating material which prevents the direct flow of charge between the bottom base and the ribbed edge. The only pathway by which charge can make it from the ribbed edge to the bottom base or vice versa is the pathway which includes the wires and the filament.

+

• The successful means of lighting the bulb involves placing the bottom base of the bulb on one terminal and connecting the ribbed edge to the other terminal using a wire.

1. There must be a closed conducting loop in the external circuit which stretches from the high potential, positive terminal to the low potential, negative terminal.

2. There must be an energy supply capable doing work on charge to move it from a low energy location to a high energy location and thus establish an electric potential difference across the two ends of the external circuit.

The Requirement of a circuit

example1. As a + charge moves through the battery from D to A, it

(gains, loses) potential energy and (gains, loses) electric potential. The point of highest energy within a battery is the (+, -) terminal.

2. As a + charge moves through the external circuit from A to D, it (gains, loses) potential energy and (gains, loses) electric potential. The point of highest energy within the external circuit is closest to the (+, -) terminal.

3. Use >, <, and = signs to compare the electric potential (V) at the four points of the circuit.

VA ____ VB_______ VC _________VD

Electric Current • If the two requirements of an electric circuit are met, then

charge will flow through the external circuit. This flow of charge or current, is the rate at which charge flows past a point on a circuit.

Current is a rate quantity. Like velocity - the rate at which an object changes its position. Acceleration - the rate at which an object changes its velocity. And power - the rate at which work is done on an object. In every case of a rate quantity, the mathematical equation involves some quantity over time.

• Electric current refers to the rate at which charge passes a given point in a circuit.

Q: the amount of charge that passes a point, in Coulombt: time, in secondsI, electric current, in ampere (A), which is a fundamental

unit. 1 A = 1 C / s

Current can only be sustained if there is difference in ELECTRICAL POTENTIAL or

VOLTAGE between two points!

tqIcurrent

:

• André-Marie Ampère (20 January 1775 – 10 June 1836) was a French physicist and mathematician who is generally regarded as one of the main discoverers of electromagnetism. The SI unit of measurement of electric current, the ampere, is named after him.

Conventional Current Direction

The direction of an electric current is by convention the direction in which a positive charge would move.

Current versus Drift Speed

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Current has to do with the number of coulombs of charge that pass a point in the circuit per unit of time.

• Drift speed refers to the average distance traveled by a charge carrier per unit of time.

Even though the drift speed is extremely slow, the current could be big. This is because there are many, many charge carriers moving at once throughout the whole length of the circuit.

The Nature of Charge Flow• We know that the average drift speed of an electron is

very, very slow, why does the light in a room or in a flashlight light immediately after the switched is turned on?

• Charge carriers in the wires of electric circuits are electrons. They are already there supplied by the atoms of the wire. Once the switch is turned to on, there is an electric potential difference established across the two ends of the external circuit. The electrons begin moving along a zigzag path in their usual direction. Thus, the flipping of the switch causes an immediate response throughout every part of the circuit, setting charge carriers everywhere in motion in the same net direction.

• While the actual motion of charge carriers occurs with a slow speed, the signal that informs them to start moving travels at a fraction of the speed of light.

• The charge carriers never become consumed or used up. While the energy possessed by the charge may be used up, the charge carriers themselves do not disintegrate, disappear or otherwise become removed from the circuit. And there is no place in the circuit where charge carriers begin to pile up or accumulate. The rate at which charge enters the external circuit on one end is the same as the rate at which charge exits the external circuit on the other end.

Check Your Understanding1. A current is said to exist whenever _____.

a. a wire is charged b. a battery is presentc. electric charges are unbalancedd. electric charges move in a loop

2. Current has a direction. By convention, current is in the direction that ___.

a. + charges move b. - electrons movec. + electrons move

3. The drift velocity of mobile charge carriers in electric circuits is ____.a. very fast; less than but very close to the speed of light b. fast; faster than the fastest car but nowhere near the speed of lightc. slow; slower than Chris Rock runs the 200-metersd. very slow; slower than a snail

4. Use the diagram to complete the following statements:a. A current of one ampere is a flow of charge at the rate of

_______ coulomb per second.b. When a charge of 8 C flows past any point along a circuit in 2

seconds, the current is ________ A.c. If 5 C of charge flow past point A (diagram at right) in 10

seconds, then the current is _________ A.d. If the current at point D is 2.0 A, then _______ C of charge

flow past point D in 10 seconds.e. If 12 C of charge flow past point A in 3 seconds, then 8 C of

charge will flow past point E in ________ seconds.f. True or False: The current at point E is considerably less than

the current at point A since charge is being used up in the light bulbs.

 

example• If charge flowing at the rate of 2.50 × 1016 elementary

charges per second. What is the electric current?

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Lesson 2: Electrical Resistance1. Journey of a Typical Electron 2. Resistance

Resistance• Resistance is the hindrance to the flow of charge. For an

electron, the journey from terminal to terminal is not a direct route. Rather, it is a zigzag path which results from countless collisions with fixed atoms within the conducting material.

• While the electric potential difference established between the two terminals encourages the movement of charge, it is resistance which discourages it.

• The rate at which charge flows (current) from terminal to terminal is the result of the combined affect of these two quantities: potential difference and resistance.

Variables Affecting Electrical Resistance - R1. The total length of the wires will affect the amount of resistance. The

longer the wire, the more resistance that there will be – R is directly proportional to length.

2. The cross-sectional area of the wires will affect the amount of resistance. The wider the wire, the less resistance that there will be to the flow of electric charge – R is inversely proportional to Area.

3. The material that a wire is made of. Some materials are better conductors than others and offer less resistance to the flow of charge. Silver is one of the best conductors but is never used in wires of household circuits due to its cost. Copper and aluminum are among the least expensive materials with suitable conducting ability to permit their use in wires of household circuits. The conducting ability of a material is resistivity.

4. The temperature. Since resistity increases with increasing temperature, the higher the temperature, the more resistance that there will be. You can find a list of resistivity values for various materials at temperatures of 20 degrees Celsius in your reference table.

Mathematical Nature of Resistance• The standard metric unit for resistance is the ohm,

represented by the Greek letter omega - Ω . The equation representing the dependency of the resistance (R) of a cylindrically shaped conductor (e.g., a wire) upon the variables which affect it is:

L represents the length of the wire (in meters), A represents the cross-sectional area of the wire (in m2), ρ represents the resistivity of the material (in Ω•meter). R represents the resistance of the wire (in Ω)

• If the length of the wire is increased, Resistance is increased – direct linear relationship.

• If the area of the wire is increased, Resistance is decreased – inverse relationship

L

R Linear

R

A

Non Linear

Graph of R vs. L and R vs. A

example

• An incandescent light bulb is supplied with a constant potential difference of 120 volts. As the filament of the bulb heats up,

1. What happens to the resistance?

2. What happens to the current?

example• Determine the resistance of a 4.00 meter length of

copper wire having a diameter of 2.00 mm. Assume a temperature of 20oC.

example

• What is the composition of a wire with a resistance of 31.8 Ohms if it is 5 x 107 meters long and has a cross-sectional area of 0.025 m2?

•What is the composition of a wire with a resistance of 31.8 Ohms if it is 5 x 107 meters long and has a cross-sectional area of 0.025 m2?

example

• If the cross-sectional area of a metallic conductor is halved and the length of the conductor is doubled, the resistance of the conductor will be ______________.

1. halved 2. doubled 3. unchanged 4. quadrupled

example• A 12.0-meter length of copper wire has a

resistance of 1.50 ohms. How long must an aluminum wire with the same cross-sectional area be to have the same resistance?

example

• Pieces of aluminum, copper, gold, and silver wire each have the same length and the same cross-sectional area. Which wire has the lowest resistance at 20°C?

• Ohm’s Law states the relationship between current, potential difference and resistance. “At constant temperature, the current in a metallic conductor is directly proportional to the potential difference between its ends, and inversely proportional to its resistance.”

• Ohm’s Law is specific for certain materials and not general law of electricity.

Lesson 3: Ohm’s law

Ohm's Law: I = V / R• Where: V = potential in volts

I = current in amperesR = resistance measured in ohms

V

R I

V = R∙I

I = V / RR = V / I

Resistance: R = V / I• Since R = V / I, we say that the resistance, R, is the

constant of proportionality in Ohm’s law.

V

I

Slope is resistance

• Resistance = ∆v / ∆I, which is the slope of a potential difference vs. current graph. The resistance is a constant for a metallic conductor at constant temperature.

V

I

Does not obey Ohm’s Law

Ohm's Law as a Predictor of Current

• This equation indicates how the two variables (potential difference and resistance) would affect the amount of current in a circuit.

• The current in a circuit is directly proportional to the electric potential difference impressed across its ends and inversely proportional to the total resistance offered by the external circuit.

• The greater the battery voltage (i.e., electric potential difference), the greater the current. a twofold increase in the battery voltage would lead to a twofold increase in the current (if all other factors are kept equal).

• The greater the resistance, the less the current. An increase in the resistance of the load by a factor of two would cause the current to decrease by a factor of two to one-half its original value.

RVI

Let’s practice: I = V / R

• Volts resistance current

1. 1.5 V 3 Ω    0.50 Amp

2. 3.0 V 3 Ω    ________

3. 4.5 V 3 Ω    ________

4. 4.5 V 6 Ω    ________

5. 4.5 V 9 Ω    ________

V and I have direct relationship

V and I have direct relationship

V and R have inverse relationship

example• The diagram below depicts a couple of circuits

containing a voltage source (battery pack), a resistor (light bulb) and an ammeter (for measuring current). In which circuit does the light bulb have the greatest resistance?

A B

Circuit

• A path through which current flows from an area of high voltage to an area of low voltage.

Circuit ElementsVoltage sources

Resistances

Measurement Devices

Other Elements

Measurements

V = 100V

R = 10Ω

V

V V

V

100V

0V

100V

0VA10A

A10A

Voltmeter measures

RELATIVE differences

from OUTSIDEthe circuit

Ammeter measures

flow INSIDEthe circuit

Graphs: I vs. V and I vs. R

I

V

Slope = ∆I / ∆V = 1/R

I

R

Current and resistance have an inverse relationship

Current and potential difference have a direct relationship. The slope is equivalent to the reciprocal of the resistance of the resistor.

I vs. V I vs. R

Check Your Understanding1. Which of the following will cause the current through an

electrical circuit to decrease? Choose all that apply.a. decrease the voltage b. decrease the resistancec. increase the voltaged. increase the resistance

2. A certain electrical circuit contains a battery with three cells, wires and a light bulb. Which of the following would cause the bulb to shine less brightly? Choose all that apply.

a. increase the voltage of the battery (add another cell) b. decrease the voltage of the battery (remove a cell)c. decrease the resistance of the circuitd. increase the resistance of the circuit

3. A circuit is wired with a power supply, a resistor and an ammeter (for measuring current). The ammeter reads a current of 24 mA (milliAmps). Determine the new current if the voltage of the power supply was ...

a. ... increased by a factor of 2 and the resistance was held constant.

b. ... increased by a factor of 3 and the resistance was held constant.

c. ... decreased by a factor of 2 and the resistance was held constant.

d. ... held constant and the resistance was increased by a factor of 2.

e. ... held constant and the resistance was increased by a factor of 4.

f. ... held constant and the resistance was decreased by a factor of 2.

g. ... increased by a factor of 2 and the resistance was increased by a factor of 2.

h. ... increased by a factor of 3 and the resistance was decreased by a factor of 2.

i. ... decreased by a factor of 2 and the resistance was increased by a factor of 2.

4. Use the Ohm's law equation to determine the missing values in the following circuits.

How is current controlled in A & B?

How is current controlled in C & D?

4

6

example• The graph shows the relationship between

current and potential difference for four resistors, A, B, C, and D . Which resistor has the greatest resistance?

example• A series circuit has a total resistance of 1.00 ×

102 ohms and an applied potential difference of 2.00 × 102 volts. What is the amount of charge passing any point in the circuit in 2.00 seconds?

example• A long copper wire was connected to a voltage source.

The voltage was varied and the current through the wire measured, while temperature was held constant. Using the graph to find the resistance of the copper wire.

example• A student conducted an experiment to determine the

resistance of a light bulb. As she applied various potential differences to the bulb, she recorded the voltages and corresponding currents and constructed the graph below. The student concluded that the resistance of the light bulb was not constant.

1. What evidence from the graph supports the student’s conclusion?

2. According to the graph, as the potential difference increased, what happens to the resistance of the light bulb?

example• A circuit consists of a resistor and a battery.

Increasing the voltage of the battery while keeping the temperature of the circuit constant would result in an increase in

1. current, only 2. resistance, only 3. both current and resistance 4. neither current nor resistance

example• Sketch a graph that best represents the

relationship between the potential difference across a metallic conductor and the electric current through the conductor

1. At constant temperature T1

2. At a higher constant temperature T2.V

I

Lesson 4: Electrical Power• Power: Putting Charges to Work • Common Misconceptions Regarding

Electric Circuits

Power: Putting Charges to Work • Electric circuits are designed to serve a useful function. The

mere movement of charge from terminal to terminal is of little use if the electrical energy possessed by the charge is not transformed into another useful form.

• To equip a circuit with a battery and a wire leading from positive to negative terminal without an electrical device (light bulb, beeper, motor, etc.) would lead to a high rate of charge flow. Such a circuit is referred to as a short circuit. It would heat the wires to a high temperature and drain the battery of its energy rather quickly.

• When a circuit is equipped with a light bulb, beeper, or motor, the electrical energy supplied to the charge by the battery is transformed into other forms in the electrical device. These electrical devices are generally referred to as a load.

• An electrical circuit is simply an energy transformation tool. Energy is provided to the circuit by an electrical energy source, and energy is delivered by the circuit to the load. The rate at which this energy transformation occurs called Power.

• Power is the rate at which electrical energy is supplied to a circuit or consumed by a load. electrical power, like mechanical power, is the rate at which work is done. Like current, power is a rate quantity. It's mathematical formula is expressed on a per time basis.

Electrical Power

• The unit of power is watt. • One watt of power is equivalent to the delivery of

1 joule of energy every second. In other words: 1 watt = 1 joule / second

• A 60 watts light bulb means 60 joules of energy delivered to the light bulb every second. A 120-watt light bulbs draws 120 joules of energy every second.

The kilowatt-hour• Electrical utility companies who provide energy for

homes provide a monthly bill charging those homes for the electrical energy which they used. A typical bill will contain a charge for the number of kilowatt-hours of electricity which were consumed.

• 1 Kilowatt = 1,000 watt, which represent power.• 1 hour = 3,600 seconds, which represent time.• A kilowatt • hour is a unit of Power • time. • Since P = E / t, therefore P• t = E. • So the kilowatt • hour is a unit of energy. • 1 Kwh = (1,000 w)(3,600 s) = 3,600,000 J

misconception• True or False?• The utility company provides electricity in the

form of electrons.

Calculating Power

• The electrical power is simply the product of the electric potential difference and the current.

When we combine the equations above, we can derive:

The two quantities that power depends upon are both related to the resistance of the load by Ohm's law.

∆V = (I • R) I = ∆V / R

By combing Ohm’s law and the equation for power (P = ∆V∙I), two new equations can be derived that relate the power to the current and the resistance and to the electric potential difference and the resistance.

P = I2 • R P = ∆V2 / R

P = I2•R relate current and resistance to power, notice double importance of current.

P = V2/R relate potential difference and resistance to power, notice double importance of potential difference.

P = V·I relate potential difference and current to power. Notice that both have equal importance.

While these three equations provide one with convenient formulas for calculating unknown quantities in physics problems, one must be careful to not misuse them by ignoring conceptual principles regarding circuits.

example• If a 60-watt bulb in a household lamp was replaced

with a 120-watt bulb, then how many times greater would the current be in that lamp circuit?

Graphs of power vs. R, I, V• P = VI = I2R = V2/R• When V is constant: P = VI; P = V2/R

• When R is constant: P = I2R; P = V2/R

P

I

P

RV is slope

Inverse, high R, low P

P P

I VDirect squared Direct squared

example

• Which is a unit of electrical power?1.volt/ampere 2.ampere/ohm 3.ampere2/ohm 4.volt2/ohm

example

• As the resistance of a constant-voltage circuit is increased, the power developed in the circuit

1.decreases 2.increases 3.remains the same

example• The potential difference applied to a circuit element remains

constant as the resistance of the element is varied. Graph power (P) vs. resistance ((R) for this circuit.

P

R

example

• Graph the relationship between the electrical power and the current in a resistor that obeys Ohm’s Law.

P

I

example• An electric motor uses 15 amperes of

current in a 440-volt circuit to raise an elevator weighing 11,000 newtons.  What is the average speed attained by the elevator?

Statement True or False?1. When an electrochemical cell no longer works, it is out of

charge and must be recharged before it can be used again.

2. An electrochemical cell can be a source of charge in a circuit. The charge which flows through the circuit originates in the cell.

3. Charge becomes used up as it flows through a circuit. The amount of charge which exits a light bulb is less than the amount which enters the light bulb.

4. Charge flows through circuits at very high speeds. This explains why the light bulb turns on immediately after the wall switch is flipped.

5. The local electrical utility company supplies millions and millions of electrons to our homes everyday.

• Rechargeable batteries has nothing to do with charges. • A battery (or single cell) operates by packing a collection of reactive

chemicals inside. These chemicals undergo a reaction that produces energy. This energy-producing reaction is capable of pumping the charge through the battery from low energy terminal to high energy terminal and establishing the electric potential difference across the external circuit. When a battery no longer works, it is because the chemicals have been consumed to the point that the ability of the battery to move the charge between terminals has been severely diminished.

• Rechargeable batteries rely upon a reversible reaction, turning the chemical products back into chemical reactants within the cell.

• By placing the cell into a so-called recharger, the energy of a household electrical circuit can be used to drive the reaction in the reverse direction and transform the chemical products back into chemical reactants. This reverse process requires energy; it is the recharger which supplies the energy. With reactants replenished, the cell can now be used again to power the electric circuit.

Rechargeable Batteries

Quantities, Symbols, Equations and Units!

• The tendency to give attention to units is an essential trait of any good physics student.

• Many of the difficulties associated with solving problems may be traced back to the failure to give attention to units. As more and more electrical quantities and their respective metric units are introduced, it will become increasingly important to organize the information in your head.

Quantity Symbol EquationsStandard

Metric Unit

Other Units

Potential Difference

(a.k.a. voltage)  V    V= W / Q

V = I • R Volt (V) J / C

Current I I = Q / t I = V / R

Amperes (A)

C / s V / Ω

Power P

P = W / t P = V∙I

P = V2/RP = I2R

Watt (W)

J / sV∙A

V/ Ω2

A2∙Ω

Resistance R R = ρ•L / A R = V / I Ohm (Ω ) V / A

Energy W W = V • Q W = P • t Joule (J) V • C

W • s

Check Your Understanding• The purpose of every circuit is to supply the energy to

operate various electrical devices. These devices are constructed to convert the energy of flowing charge into other forms of energy (e.g., light, thermal, sound, mechanical, etc.). Use complete sentences to describe the energy conversions that occur in the following devices.

a. Windshield wipers on a car b. Defrosting circuit on a carc. Hair dryer    

example

• To increase the brightness of a desk lamp, a student replaces a 60-watt light bulb with a 100-watt bulb.  Compared to the 60-watt bulb, the 100-watt bulb has

1.less resistance and draws more current 2.less resistance and draws less current 3.more resistance and draws more current 4.more resistance and draws less current

1. Which would be thicker (wider) - the filament of a 60-Watt light bulb or the filament of a 100-W light bulb? Explain.

 

 2. Calculate the resistance and the current of a 7.5-Watt night light

bulb plugged into a US household outlet (120 V).  

Check Your Understanding

Electrical energy

• E = P∙t = V∙I∙t = I2∙R∙t = (V2/R)∙t • The SI unit for energy is ___________.• 1 joule = (1 Newton)(1 meter)

= (1 kg∙m/s2)(1 meter)= 1 kg∙m2/s2

joule

• Your 60-watt light bulb is plugged into a 110-volt household outlet and left on for 10 hours. The utility company charges you $0.20 per kiloWatt•hr. What is the cost of such a mistake.

example

example

• A current of 0.40 ampere is measured in a 150 ohm resistor, how much energy is expended by the resistor in 20. seconds?

example

• An operating 75-watt lamp is connected to a 120-volt outlet.  How much electrical energy is used by the lamp in 60. minutes (3600 seconds)?

example

• An electric dryer consumes 6.0 × 106 joules of energy when operating at 220 volts for 30. minutes (1800 seconds). During operation, how much current does the dryer draws approximately?

example• 50.-ohm resistor, an unknown resistor R, a 120-volt source, and

an ammeter are connected in a complete circuit. The ammeter reads 0.50 ampere. Calculate the power dissipated by the 50.-ohm resistor.

example• The heating element on an electric stove

dissipates 4.0 × 102 watts of power when connected to a 120-volt source.  What is the electrical resistance of this heating element?

3/6 DO NOW

• A copper wire is connected across a constant voltage source. The current flowing in the wire can be increased by increasing the wire's

1. cross-sectional area 2. length 3. resistance 4. temperature

objectives

• Circuit connections

• No post today

Lesson 4: Circuit Connections

1. Circuit Symbols and Circuit Diagrams 2. Two Types of Connections 3. Series Circuits 4. Parallel Circuits

Circuit SymbolsVoltage sources

Resistances

Measurement Devices

Other Elements

Example 1: Description with Words: • Three D-cells are placed in a battery pack to

power a circuit containing three light bulbs

Only use circuit symbols in your reference table to draw the circuits

Example 2: • Description with Words: Three D-cells are

placed in a battery pack to power a circuit containing three light bulbs.

Two types of connections• These two examples illustrate the two common

types of connections made in electric circuits. When two or more resistors are present in a circuit, they can be connected in series or in parallel.

Lab 27 – two types of circuits• Go to: http://phet.colorado.edu/en/simulation/circuit-

construction-kit-dcPurpose: compare series and parallel circuitsMaterial: computer1. Draw schematic diagrams for series and parallel circuits

consisting of 3 light bulbs.2. As the light bulbs are added, what happens to the

current going to the battery3. As the light bulbs are added, what happens to the total

resistance of the circuit?4. If one light bulb is taken out, what happens to the other

light bulbs?

For series circuits1. As more resistors are added the overall

current within the circuit decreases. 2. This decrease in current is consistent with the

conclusion that the overall resistance increases.

3. If one of three bulbs in a series circuit is unscrewed from its socket, then the other bulbs immediately go out.

For parallel circuits1. As the number of resistors increases, the

overall current also increases. 2. This increase in current is consistent with a

decrease in overall resistance. Adding more resistors in a separate branch has the unexpected result of decreasing the overall resistance!

3. If an individual bulb in a parallel branch is unscrewed from its socket, then there is still current in the overall circuit and current in the other branches.

The effect of adding resistors• Adding more resistors in series means

that there is more overall resistance; • Adding more resistors in parallel means

that there is less overall resistance.

Check Your Understanding1. Observe the electrical wiring below. Indicate whether

the connections are series or parallel connections. Explain each choice.

                                                                                                             

2. Two electric circuits are diagrammed below. For each circuit, indicate which two devices are connected in series and which two devices are connected in parallel.

In series? ______________ In parallel? ______________

In series ________________ In parallel? ______________

Series circuit• A series circuit is a circuit in which all parts are

connected end to end to provide a ___________ path for the current.

• The figure shows three resistors connected in series with a battery. The resistors are differentiated by the use of subscripts R1, R2, and R3.

single

Adding more resistors to a series circuit results in more overall resistance.

This increased resistance serves to reduce the rate at which charge flows (also known as the current).

• Since there is only one current path in a series circuit, the current is the same through each resistor.

• ______________________

Current

Charge flows together through the external circuit at a rate which is everywhere the same. The current is no greater at one location as it is at another location.

Ibattery = I1 = I2 = I3 = ..

Equivalent Resistance• The equivalent resistance of a circuit is the amount of

resistance which a single resistor would need in order to equal the overall affect of the collection of resistors which are present in the circuit.

•The equivalent resistance in a series circuit is the sum of the circuit’s resistances:

____________________________________Req = R1 + R2 + R3 + ...

Potential Difference and Voltage Drops

• The sum of the potential differences across the individual resistors equals the applied potential difference at the terminals.

• _______________________________∆Vbattery = ∆V1 + ∆V2 + ∆V3 + ...

Mathematical Analysis of Series Circuits

Ibattery= I1 = I2 = I3 = ...

Req = R1 + R2 + R3 + ...Vbattery =  V1 +  V2 +  V3 + ...

V1 = I • R1     V2 = I • R2     V3 = I • R3V1

V2

V3

• All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law

example

40 1.5

1.5

1.5

1.5

25.5

18

16.5

example• The diagram represents a series circuit

containing three resistors. What is the current through resistor R2?

I = V / R = 3.0 V / 9.0 Ω

I = 0.33 A

example

• In the circuit shown in the diagram, what is the correct reading for meter V2?

V = V1 + V2 + V3

110 V = 20 V + V2 + 20 VV2 = 70 V

example• A series circuit has a total resistance of

1.00 x 102 ohms and an applied potential difference of 2.00 x 102 volts. What is the amount of charge passing any point in the circuit in 2.00 seconds?

I = V / R = 2.00 x 102 V / 1.00 x 102 Ω

I = 2.00 A

I = Q / t

2.00 A = Q / 2.00 s Q = 4.00 C

3/7 do now1. Draw a schematic diagrams for series circuits consisting

of 3 lamps.2. As lamps are added, what happens to the total current

going to the battery.3. As lamps are added, what happens to the total

resistance of the circuit?4. If one lamp is taken out, what happens to the other light

lamps?

Homework questions?

objectives

• Series circuits

• Parallel circuits

• Lesson 4, 5 quiz on castle learning – due Monday

One by One

Series Circuits

Series CircuitA circuit composed of two or more elements

connected end-to-end.

Rules• The equivalent resistance for a series circuit is the

SUM of all RESISTANCES in the circuit• Req = R1 + R2 + R3 + …+ RN

• The total voltage in the circuit is equal to the SUM of the VOLTAGE DROPS across the resistors.

• VT = V1 +V2 + V3 + …+ VN

• The current in the circuit is constant at ALL points in the circuit.

• IT = I1 = I2 = I3 = …= IN

• All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law

10 V

100 Ω 75 Ω 225 Ω

Req = R1 + R2 + R3 = 400Ω

R1 R2 R3

I = V / RI = 10 V / 400 Ω

I = 0.025 A

VIRP ChartV I R P

R1 100Ω

R2 75Ω

R3 225Ω

Req 10V 0.025A 400Ω

0.025A

0.025A

0.025A

2.5V

1.875V

5.625V

0.063W

0.047W

0.14W

0.25W

? V

50 Ω 120 Ω 150 Ω

R1 R2 R3

1.5A

VIRP ChartV I R P

R1 50Ω

R2 120Ω

R3 150Ω

Req 1.5A

1.5A

1.5A

1.5A

320Ω

75 V

180 V

225 V

480 V

112.5W

270.0W

337.5W

720W

homework

• Practice packet page 28-30• Due tomorrow – pp. 23-30

• Check List Packet – (please label you packet) – pp. 1-3

3/11 do now – on a new sheet

V I R P

R1 50Ω

R2 100Ω

R3 150Ω

Req 1.0A

R1, R2, and R3 are connected in a series circuit with the following given quantities. Fill in the missing data.

objectives• Homework due – pp. 23-30• Lab – series circuits• Parallel circuits

• Homework – pp. 31-34

• T-shirt money is due ASAP

Parallel circuits• A parallel circuit is a circuit in which If two

or more circuit components are connected like the _______________________.

• Unlike in series circuit, there is just one path for current flow, in a parallel circuit, there are ____________________ paths for current flow.

rungs of a ladder.

two or more

1. More current flows through the smaller resistor. (More charges take the easiest path.)

2. The potential difference of different resistors are the same, they all have the same drop.

3. By the time each charge makes it back to the battery, it has lost all the electrical energy given to it by the battery.

Current• In a parallel circuit, charge divides up into separate

branches such that there can be more current in one branch than there is in another. Nonetheless, when taken as a whole, the total amount of current in all the branches when added together is the same as the amount of current at locations outside the branches.

• In equation form, this principle can be written as• Itotal = I1 + I2 + I3 + ...

• where Itotal is the total amount of current outside the branches (and in the battery) and I1, I2, and I3 represent the current in the individual branches of the circuit.

• At any junction in a circuit, the sum of the currents entering the junction must equal the sum of current leaving it.

This is the symbol for an ammeter - a device used to measure the current at a specific point. An ammeter is capable of measuring the current while offering negligible resistance to the flow of charge.

Kirchhoff’s law - conservation of charge(Junction Rule)

• The sum entering any current junction, is equal to the sum leaving. A represents a junction in an electric circuit. Nine amperes are entering A: therefore, according to Kirchhoff’s First Law, nine amperes must come out of junction A.

A9 amp

6 amp

3 amp

example• The diagram shows the current in three of the branches

of a direct current electric circuit. The current in the fourth branch, between junction P and point W, must be

1. 1 A toward point W 2. 1 A toward point P 3. 7 A toward point W 4. 7 A toward point P  

example

• The diagram shows a current in a segment of a direct current circuit.  What is the reading of ammeter A?

example

• The diagram below represents currents in a segment of an electric circuit.

• What is the reading of ammeter A?

Equivalent Resistance • For parallel circuit, adding more resistors results in the

rather unexpected result of having less overall resistance.

• The equivalent resistance (total resistance) of a circuit is the amount of resistance which a single resistor would need in order to equal the overall effect of the collection of resistors which are present in the circuit. For parallel circuits, the mathematical formula for computing the equivalent resistance (Req) is

where R1, R2, and R3 are the resistance values of the individual resistors which are connected in parallel.

321

1111RRRReq

example

Note: the equivalent resistance is less than any single resistance in the circuit.

1/Req = 1/(5.0 Ω) + 1/(7.0 Ω) + 1/(12 Ω)

Req = 2.3 Ω

example

• Which circuit segment below has the same total resistance as the circuit segment shown in the diagram?

1 2 3 4

example• Resistors R1 and R2 have the same resistance.

When they are connected together as shown, they have an equivalent resistance of 4 ohms.  What is the resistance of R1?

Since R1 = R2

1/4 Ω = 1/R1 + 1/R1 = 2/R1

R1 = 8 ΩNote: the equivalent resistance is smaller than any single resistance in the parallel circuit.

example• Resistors R1 and R2 have an equivalent

resistance of 6 ohms when connected as shown.  What is the resistance of R1?

1. 3 ohms2. 4 ohms3. 5 ohms4. 8 ohmsSince the equivalent resistance is smaller than any single resistance in the parallel circuit, the answer is 8 ohms

Voltage Drops for Parallel Branches• The total voltage drop in the external circuit is equal to

the gain in voltage as a charge passes through the internal circuit. In a parallel circuit, a charge does not pass through every resistor; rather, it passes through a single resistor. Thus, the entire voltage drop across that resistor must match the battery voltage. It matters not whether the charge passes through resistor 1, resistor 2, or resistor 3, the voltage drop across the resistor which it chooses to pass through must equal the voltage of the battery. Put in equation form, this principle would be expressed as

Vbattery = V1 = V2 = V3 = ..

• The current through a given branch can be predicted using the Ohm's law equation and the voltage drop across the resistor and the resistance of the resistor. Since the voltage drop is the same across each resistor, the factor which determines which resistor has the greatest current is the resistance. The resistor with the greatest resistance experiences the lowest current and the resistor with the least resistance experiences the greatest current. In this sense, it could be said that charge (like people) chooses the path of least resistance. In equation form, this could be stated as

I1 = V / R1

I2 = V / R2

I3 = V / R3

In a parallel circuit:1. The potential drops of each branch equals the potential

rise of the source.

2. The total current is equal to the sum of the currents in the branches.

3. The inverse of the total resistance of the circuit (also called equivalent resistance) is equal to the sum of the inverses of the individual resistances.

4. All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law

example• Find the voltage drop R1, R2, and R3

• Find the current in R1, R2, and R3

example

4.3 14.0

3.5

5.0

5.5

60.

60.

60.

example

• A 9.0 V battery is connected in parallel to four light bulbs with resistances 4.0Ω, 5.0Ω, 2.0Ω, and 7.0Ω. Find the equivalent resistance for the circuit and the total current in the circuit.

Req = 0.92 Ω

I = 9.8 A

example• What are the readings on the volt meters in A & B?

A B

Parallel circuits,

VT = V1 = V2 = 6 V

Series circuits, VT = V1 + V2 = 6 V; I1 = I2; V1 /R1 = V2 / R2; V1 /20 = V2 /40 V1 = 2 Volts

example

• In the diagram, what is the potential difference across the 3.0-ohm resistor?

3/12 do now• The diagram represents a series circuit

containing three resistors. What is the current through resistor R2?

Homework questions?

Show work

objectives

• Parallel circuits• Meters in a circuits

• Homework – practice packet pp. 35-40

example• Circuit A and circuit B are shown in the

diagram. Compared to the total resistance of circuit A, the total resistance of circuit B is

1. less 2. greater 3. the same

example• A physics student is given three 12-ohm

resistors with instructions to create a circuit that would have the lowest possible resistance.  The correct circuit would be

1. a series circuit with a total resistance of 36 ohms

2. a series circuit with a total resistance of 4 ohms 3. a parallel circuit with a total resistance of 36

ohms 4. a parallel circuit with a total resistance of 4

ohms

Meters in a circuit• Ammeters, as well as voltmeters and

ohm-meters, are designed with the use of a _______________________, which is sensitive electric current detector.

• When a current is passed through a coil in a magnetic field, the coil experiences a torque proportional to the current.

galvanometer

Meters in a circuit• An ammeter is used to measure ____________• An ammeter is always connected in __________ with the

circuit element being measured• A voltmeter is used to measure

________________________________• A voltmeter is always connected in __________.

current series

potential difference. parallel.

ammeter• An ammeter is placed in series with a

circuit element to measure the electric current flow through it. The meter must be designed offer ________________ resistance to the current so that it does not change the circuit it is measuring.

very little

example• In the diagram of a parallel circuit,

ammeter A measures the current supplied by the 110-volt source.  What is the current measured by ammeter A?

11 A

example• Two resistors are connected to a source of

voltage as shown in the diagram. At which position should an ammeter be placed to measure the current passing only through resistor R1?

1.   position 1 2.   position 2 3.   position 3 4.   position 4

example• Three ammeters are placed in a circuit as

shown in the diagram.  If A1 reads 5.0 amperes and A2 reads 2.0 amperes, what does A3 read?

3 A

voltmeter• A voltmeter is placed in parallel with a circuit element to

measure the voltage drop across it and must be designed to draw very little current from the circuit so that it does not appreciably change the circuit it is measuring. A voltmeter has a big resistance, so it does not affect the overall circuit.

example

• In the circuit shown in the diagram, which is the correct reading for meter V2?

example• Which circuit could be used to determine the

total current and potential difference of a parallel circuit?

A B

C D

example

• In the circuit shown in the diagram, what is the potential difference of the source?

meters

Read current, connected in series, very low resistance

Read potential difference, connected in parallel, very high resistance

ammeter

voltmeter

Wiring for Voltage

Parallel Circuits

Parallel CircuitsA circuit in which all of the resistors are connected “in parallel”

to the same voltage source.

Note: in this animation that the charges have the same potentialbefore and after they pass through the resistors!

Parallel CircuitsThe charges fall through the 30Ω resistor at a slower rate.Less CURRENT flows through that branch of the circuit!

The CURRENT flowing into and out of the BATTERYis the same!

Rules• The inverse of the equivalent resistance is the sum of

the INVERSES OF EACH RESISTANCE

• The total current in the circuit is equal to the SUM of the CURRENT passing through each resistor.

• The voltage is the same for ALL resistors in the circuit.

• All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law

Neq RRRRR1...1111

321

NIIIII ...321

NVVVVV ...321

Junction Rule

The total current flowing INTO a junction of two or morewires is the SAME as the total current flowing OUT

of the junction.

5A

10A ?5A

Junction Rule

6A

2A

10A?6A ?4A

V I R PR1

30 Ω

R230 Ω

R330 Ω

Req60 V R1 = 30 Ω

R2 = 30 Ω

R3 = 30 Ω

60 V

60 V

60 V

60 V

2 A

2 A

2 A

6 A 10 Ω

120W

120 W

120 W

360W

V I R PR1

70 Ω

R260 Ω

R350 Ω

ReqR1 = 70 Ω

R2 = 60 Ω

R3 = 50 Ω

? V

2.5 V

2.5 V

2.5 V

0.036A

0.042A

0.05A

0.128A 19.62 Ω2.5 V

0.05 A 0.09W

0.11 W

0.13 W

0.32W

3/13 do now• A lamp and an ammeter are connected to a source as

shown in the diagram. What is the electrical energy expended in the lamp in 3.0 seconds? [show work]

objectives• Homework questions - Packet pp. 31-40 is

due

• Finish series circuits lab

• Homework: Electric current check list

• Castle learning quiz – due Friday• Electromagnetism Unit Test is on Tuesday

example• Which circuit below would have the lowest

voltmeter reading?

A B

C D

example• In which pair of circuits shown in the diagram could the

readings of voltmeters V1 and V2 and ammeter A be correct?

1. A and B 2. B and C 3. C and D 4. A and D

example

• In the circuit diagram below, what are the correct readings of voltmeters V1 and V2?

                                                     

6 V

example• Which statement about ammeters and voltmeters is

correct?1. The internal resistance of both meters should be low. 2. Both meters should have a negligible effect on the

circuit being measured. 3. The potential drop across both meters should be

made as large as possible. 4. The scale range on both meters must be the same.

example• In the diagram below, lamps L1 and L2 are

connected to a constant voltage power supply. If lamp L1 burns out,

1. What will happen to the equivalent resistance of the circuit?

2. What will happen to the total current of the circuit?

3. What will happen to the brightness of L2 ?

example• Identical resistors (R) are connected across the same

12-volt battery. Which circuit uses the greatest power?

BA

C D

• Three identical light bulbs are connected to a D-cell as shown below. P, Q, X, Y and Z represent locations along the circuit. Which one of the following statements is true?

a. The current at Y is greater than the current at Q.

b. The current at Y is greater than the current at P.

c. The current at Y is greater than the current at Z.

d. The current at P is greater than the current at Q.

e. The current at Q is greater than the current at P.

f. The current is the same at all locations.

• Three identical light bulbs are connected to a D-cell as shown below. P, Q, X, Y and Z represent locations along the circuit. At which location(s), if any, will the current be ...

a. ... the same as at X? b. ... the same as at Q?c. ... the same as at Y?d. ... less than at Q?e. ... less than at P?f. ... twice that at Z?g. ... three times that at Y?

• Which adjustments could be made to the circuit below that would decrease the current in the cell? List all that apply.

a. Increase the resistance of bulb X. b. Decrease the resistance of bulb X.c. Increase the resistance of bulb Z.d. Decrease the resistance of bulb Z.e. Increase the voltage of the cell (somehow).f. Decrease the voltage of the cell (somehow).g. Remove bulb Y.

• Draw a diagram that shows voltmeter V and ammeter A correctly positioned to measure the total current of the circuit and the potential difference through each resistor.

A

V

Lab 28 – investigating series circuitObjective: to study the relationships among resistance, voltage, and

current when resistors are connected in a series circuit.Material: D.C. power supply, resistance board, D.C ammeter,

multipurpose meter, connecting wires.Procedure: Briefly describe how the lab is going to be done. Draw

diagrams to show how to measure each variable (one diagram for each rariable). Someone who was not present during the lab should be able to understand how the experiment was perforem and be able to reporduce the results by reading your procedure

Data section: should contain colomns of measured and calculated data. The columns should be labeled; units should be identified.

Conclusion: The Conclusion should (as always) answer the questions posed in the Purpose:1. How does the total resistance and resistance in RD, RE, RF

compare?2. How does the total current and current in RD, RE, RF compare? 3. How does the total voltage and voltage drop in RD, RE, RF

compare?

data tableCurrent (A) Voltage (V) Resistance

(ohms)Resistor DResistor EResistor F

equivalent

DEF

R

DEF

R

DEF

R

DEF

R

Resistance in D

Total resistance

Resistance in E

Resistance in F

Measuring resistance

Source

DEF

V

Source

DEF

Source

DEF

V

Source

DEF

V

Voltage in D

Voltage in E

Voltage in F

Total Voltage

VMeasuring voltage

SourceA

DEF

Source

ADEF

Source

DEF

Source

DEF

A A

Total current

Current in D

Current in E

Current in F

Measuring current

3/13 do now• A lamp and an ammeter are connected to a source as

shown in the diagram. What is the electrical energy expended in the lamp in 3.0 seconds? [show work]

objectives• Homework questions - Packet pp. 31-40 is due

• Finish series circuits lab

• Homework: Electric current check list

• Castle learning quiz – due Friday• Electromagnetism Unit Test is on Tuesday and

Wednesday.

• T-shirt money is due! (Anyone want to buy T-shirt?)

Lab 30 – investigating parallel circuitObjective: to study the relationships among resistance, voltage, and current

when resistors are connected in a parallel circuit.Material: Computer, PHeT wet siteProcedure: Go to PHeT website, construct a parallel circuits with 3

different resistors, RD, RE, RF . Copy the diagram in your lab note book.,. Measure total current and current in each resistor with ammeters, indicate ammeter in your diagram. Measure total voltage and voltage across each resistor with a voltmeter and indicate voltmeter in your diagram.

Data section: should contain colomns of measured and calculated data. The columns should be labeled; units should be identified.

Conclusion: The Conclusion should (as always) answer the questions posed in the Purpose:

1. How does the total resistance and resistance in RD, RE, RF compare?2. How does the total current and current in RD, RE, RF compare? 3. How does the total voltage and voltage drop in RD, RE, RF compare?

Lab 20 data tableCurrent (A) Voltage (V) Resistance

(ohms)Resistor DResistor EResistor F

equivalent

3/11 do now – on a new sheet

V I R P

R1 50Ω

R2 100Ω

R3 150Ω

Req 1.0A

R1, R2, and R3 are connected in a series circuit with the following given quantities. Fill in the missing data.

objectives• Homework due – pp. 23-30• Meters in circuits

• Homework – pp. 31-34

• T-shirt money is due ASAP• Castle learning quiz is due today