Chapter 18Chapter 18

Direct Current CircuitsDirect Current Circuits

Electric CircuitsElectric Circuits

An An electric circuitelectric circuit is a path through is a path through which charges can be conducted.which charges can be conducted.

A A loadload is any element in a circuit is any element in a circuit that dissipates energy (eg battery, that dissipates energy (eg battery, resistor, bulb). Wires have negligible resistor, bulb). Wires have negligible resistance so we will not classify resistance so we will not classify them as a loadthem as a load

Closed and Open CircuitsClosed and Open Circuits

In a In a closed circuitclosed circuit there is a closed- there is a closed-loop path for electrons to follow. A loop path for electrons to follow. A closed circuit must be present for closed circuit must be present for continuous current to exist.continuous current to exist.

In an In an open circuitopen circuit there is not a there is not a complete path and therefore no complete path and therefore no charge flow nor current.charge flow nor current.

Sources of emfSources of emf

The source that maintains the The source that maintains the current in a closed circuit is called a current in a closed circuit is called a source of source of emf (electromotive force)emf (electromotive force)– Any devices that increase the potential Any devices that increase the potential

energy of charges circulating in circuits energy of charges circulating in circuits are sources of emfare sources of emf

– Examples include batteries and Examples include batteries and generatorsgenerators

emf and Internal Resistanceemf and Internal Resistance

A real battery has A real battery has some internal some internal resistanceresistance

Therefore, the Therefore, the terminal voltage is terminal voltage is not equal to the not equal to the emfemf

More About Internal More About Internal ResistanceResistance

The schematic The schematic shows the internal shows the internal resistance, rresistance, r

The terminal The terminal voltage, ΔV = Vvoltage, ΔV = Vbb-V-Vaa

ΔV = ε – IrΔV = ε – Ir IR = ε – IrIR = ε – Ir For the entire For the entire

circuit, ε = IR + Ircircuit, ε = IR + Ir

Resistors in SeriesResistors in Series

When two or more resistors are When two or more resistors are connected end-to-end, they are said to connected end-to-end, they are said to be in be in seriesseries

The current is the same in resistors The current is the same in resistors because any charge that flows through because any charge that flows through one resistor flows through the otherone resistor flows through the other

The sum of the potential differences The sum of the potential differences across the resistors is equal to the across the resistors is equal to the total potential difference across the total potential difference across the combinationcombination

Resistors in Series, contResistors in Series, cont Potentials addPotentials add

– ΔV = IRΔV = IR11 + IR + IR22 = I = I (R(R11+R+R22))

– Consequence of Consequence of Conservation of EnergyConservation of Energy

Equivalent Resistance – Equivalent Resistance – SeriesSeries

RReqeq = R = R11 + R + R22 + R + R33 + … + … The equivalent resistance of a series The equivalent resistance of a series

combination of resistors is the combination of resistors is the algebraic sum of the individual algebraic sum of the individual resistances and is always greater resistances and is always greater than any of the individual resistancethan any of the individual resistance

Equivalent Resistance – Equivalent Resistance – SeriesSeries

An ExampleAn Example

Four resistors are replaced with their Four resistors are replaced with their equivalent resistanceequivalent resistance

Ex. 1Ex. 1

A 5 ohm, 10 ohm, and 15 ohm A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series.resistor are connected in series.

A)A) Which resistor has the most current in Which resistor has the most current in it?it?

B)B) Which resistor has the largest potential Which resistor has the largest potential difference?difference?

C)C) What is the equivalent (or total) What is the equivalent (or total) resistance of the circuit?resistance of the circuit?

A 5 ohm, 10 ohm, and 15 ohm resistor A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series to a are connected in series to a

batterybattery. . Which resistor has the Which resistor has the

most current passing through it?most current passing through it?

5 ohm

10 ohm

15 ohm

All have th

e s...

0% 0%0%0%

1.1. 5 ohm5 ohm

2.2. 10 ohm10 ohm

3.3. 15 ohm15 ohm

4.4. All have the All have the same currentsame current

A 5 ohm, 10 ohm, and 15 ohm resistor A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series to a are connected in series to a

batterybattery. . Which resistor has the Which resistor has the largest potential difference across largest potential difference across

it?it?

5 ohm

10 ohm

15 ohm

All have th

e s...

0% 0%0%0%

1.1. 5 ohm5 ohm

2.2. 10 ohm10 ohm

3.3. 15 ohm15 ohm

4.4. All have the All have the same potential same potential differencedifference

When you add the potential When you add the potential differences across each resistor, differences across each resistor,

what is the relationship to the total what is the relationship to the total voltage?voltage?

Individual

vol...

Individual

vol...

Individual

vol...

0% 0%0%

1.1. Individual Individual voltages are voltages are greatergreater

2.2. Individual Individual voltages are all voltages are all equivalentequivalent

3.3. Individual Individual voltages add to voltages add to equal the totalequal the total

A 5 ohm, 10 ohm, and 15 ohm resistor A 5 ohm, 10 ohm, and 15 ohm resistor are connected in series to a are connected in series to a

batterybattery. . What is the equivalent What is the equivalent

resistance of the circuit?resistance of the circuit?

5 ohms

10 ohms

15 ohms

30 ohms

40 ohms

0% 0% 0%0%0%

1.1. 5 ohms5 ohms

2.2. 10 ohms10 ohms

3.3. 15 ohms15 ohms

4.4. 30 ohms30 ohms

5.5. 40 ohms40 ohms

Ex. 2Ex. 2

Find the current and potential Find the current and potential difference across each of the difference across each of the resistors in the following circuits:resistors in the following circuits:

A)A) A 2 ohm and a 4 ohm resistor wired in A 2 ohm and a 4 ohm resistor wired in series with a 12V sourceseries with a 12V source

B)B) A 4 ohm and a 12 ohm resistor wired in A 4 ohm and a 12 ohm resistor wired in series with a 12V sourceseries with a 12V source

C)C) A 150 ohm and a 180 ohm resistor A 150 ohm and a 180 ohm resistor wired in series with a 12V sourcewired in series with a 12V source

Resistors in ParallelResistors in Parallel

Analogy: Students leaving an assembly –Analogy: Students leaving an assembly –paths equal doors open, charges equal paths equal doors open, charges equal studentsstudents

The more doors that are open, the less the The more doors that are open, the less the total resistance istotal resistance is

The more doors that are present mean that The more doors that are present mean that less students pass through each door.less students pass through each door.

The potential difference across each resistor The potential difference across each resistor is the same because each is connected is the same because each is connected directly across the battery terminalsdirectly across the battery terminals

Kirchoff’s LawKirchoff’s Law

Kirchoff’s Law: Kirchoff’s Law: The current, I, that enters The current, I, that enters a point must be equal to the total current a point must be equal to the total current leaving that pointleaving that point– I = II = I11 + I + I22

– The currents are generally not the sameThe currents are generally not the same– Consequence of Conservation of ChargeConsequence of Conservation of Charge

Equivalent Resistance – Equivalent Resistance – Parallel, ExamplesParallel, Examples

Equivalent resistance replaces the two original Equivalent resistance replaces the two original resistancesresistances

Household circuitsHousehold circuits are wired so the electrical are wired so the electrical devices are connected in paralleldevices are connected in parallel– Circuit breakers may be used in series with other Circuit breakers may be used in series with other

circuit elements for safety purposescircuit elements for safety purposes

Equivalent Resistance – Equivalent Resistance – ParallelParallel

Equivalent Equivalent ResistanceResistance

****The equivalent ****The equivalent resistance is resistance is always less than always less than the smallest the smallest resistor in the resistor in the groupgroup

321eq R

1

R

1

R

1

R

1

Ex. 3Ex. 3

Find the current and potential Find the current and potential difference across each of the difference across each of the resistors in the following circuits:resistors in the following circuits:

A)A) A 2 ohm and a 4 ohm resistor wired in A 2 ohm and a 4 ohm resistor wired in parallel with a 12V sourceparallel with a 12V source

B)B) A 4 ohm and a 12 ohm resistor wired in A 4 ohm and a 12 ohm resistor wired in parallel with a 12V sourceparallel with a 12V source

Ex. 4Ex. 4

Find the equivalent resistance, the Find the equivalent resistance, the current in each resistor, and the current in each resistor, and the current drawn by the circuit load for current drawn by the circuit load for a 9.0V battery connected in parallel a 9.0V battery connected in parallel to the following resistors.to the following resistors.

A) two 30 ohm resistorsA) two 30 ohm resistors B) three 30 ohm resistorsB) three 30 ohm resistors C) five 30 ohm resistorsC) five 30 ohm resistors

Ex. 5Ex. 5

Sketch as many different circuits as Sketch as many different circuits as possible involving a battery and possible involving a battery and three bulbs of equal resistance.three bulbs of equal resistance.

How many different circuits would How many different circuits would exist with four bulbs?exist with four bulbs?

Problem-Solving Strategy, 3Problem-Solving Strategy, 3

A complicated circuit consisting of several A complicated circuit consisting of several resistors and batteries can often be resistors and batteries can often be reduced to a simple circuit with only one reduced to a simple circuit with only one resistorresistor– Replace any resistors in series or in parallel Replace any resistors in series or in parallel

using steps 1 or 2. using steps 1 or 2. – Sketch the new circuit after these changes Sketch the new circuit after these changes

have been madehave been made– Continue to replace any series or parallel Continue to replace any series or parallel

combinations combinations – Continue until one equivalent resistance is Continue until one equivalent resistance is

foundfound

Problem-Solving Strategy, 4Problem-Solving Strategy, 4

If the current in or the potential If the current in or the potential difference across a resistor in the difference across a resistor in the complicated circuit is to be complicated circuit is to be identified, start with the final circuit identified, start with the final circuit found in step 3 and gradually work found in step 3 and gradually work back through the circuitsback through the circuits– Use ΔV = I R and the procedures in Use ΔV = I R and the procedures in

steps 1 and 2steps 1 and 2

QUICK QUIZ 18.3With the switch in this circuit (figure a) open, there is no current in R2. There is current in R1 and this current is

measured with the ammeter at the right side of the circuit. If the switch is closed (figure b), there is current

in R2. When the switch is closed, the reading on the ammeter (a) increases, (b) decreases, or (c) remains the

same.

QUICK QUIZ 18.3 ANSWER

(a). When the switch is closed, resistors R1 and R2 are in parallel, so that the

total circuit resistance is smaller than when the switch was open. As a result,

the total current increases.

QUICK QUIZ 18.4You have a large supply of lightbulbs and a battery. You start with one lightbulb connected to the battery and notice its brightness. You then add one lightbulb at a time, each new bulb being added in

parallel to the previous bulbs. As the lightbulbs are added, what happens (a) to

the brightness of the bulbs? (b) to the current in the bulbs? (c) to the power

delivered by the battery? (d) to the lifetime of the battery? (e) to the terminal

voltage of the battery? Hint: Do not ignore the internal resistance of the

battery.

QUICK QUIZ 18.4 ANSWER

(a) The brightness of the bulbs decreases

(b) The current in the bulbs decreases

(c) The power delivered by the battery increases

(d) The lifetime of the battery decreases

(e) The terminal voltage of the battery decreases

Equivalent Equivalent Resistance – Resistance –

Complex Complex CircuitCircuit

Electrical SafetyElectrical Safety

Electric shock can result in fatal burnsElectric shock can result in fatal burns Electric shock can cause the muscles Electric shock can cause the muscles

of vital organs (such as the heart) to of vital organs (such as the heart) to malfunctionmalfunction

The degree of damage depends onThe degree of damage depends on– the magnitude of the currentthe magnitude of the current– the length of time it actsthe length of time it acts– the part of the body through which it the part of the body through which it

passespasses

Effects of Various CurrentsEffects of Various Currents

5 mA or less5 mA or less– can cause a sensation of shockcan cause a sensation of shock– generally little or no damagegenerally little or no damage

10 mA10 mA– hand muscles contracthand muscles contract– may be unable to let go a of live wiremay be unable to let go a of live wire

100 mA 100 mA – if passes through the body for 1 second or less, if passes through the body for 1 second or less,

can be fatalcan be fatal

Ground WireGround Wire

Electrical Electrical equipment equipment manufacturers use manufacturers use electrical cords electrical cords that have a third that have a third wire, called a wire, called a groundground

Prevents shocksPrevents shocks

Ground Fault Circuit Ground Fault Circuit Interrupters (GFCI)Interrupters (GFCI)

Special power outletsSpecial power outlets Used in hazardous areasUsed in hazardous areas Designed to protect people from Designed to protect people from

electrical shockelectrical shock Senses currents (of about 5 mA or Senses currents (of about 5 mA or

greater) leaking to groundgreater) leaking to ground Shuts off the current when above this Shuts off the current when above this

levellevel