SPH3UElectricity & Circuits

Overview• Electric Energy & Circuits

• Electric Charge & Electrical Structure of Matter• Electric Potential• Electric Current• Resistance• Electric Power & Energy• Series Circuits• Parallel Circuits• Complex Circuits

Reviewing Terms

Series Circuits

• In series circuits, current can only take one path.

• The amount of current is the same at all points in a series circuit.

Resistance in Series

• Each resistance in a series circuit adds to the total resistance of the circuit.

Rtotal = R1 + R2 + R3...

Resistance in Series

• Light bulbs, resistors, motors, and heaters usually have much greater resistance than wires and batteries.

Example #1

• How much current flows in a circuit with a 1.5-volt battery and three 1 ohm resistances (bulbs) in series?

Voltage in a Series Circuit

• Each separate resistance creates a voltage drop as the current passes through.

• As current flows along a series circuit, each type of resistor transforms some of the electrical energy into another form of energy.

• Ohm’s law is used to calculate the voltage drop across each resistor.

Kirchoff’s Voltage Law

Parallel Circuits

• In parallel circuits the current can take more than one path.

• Because there are multiple branches, the current is not the same at all points in a parallel circuit.

Parallel Circuits

• Sometimes these paths are called branches.

• The current through a branch is also called the branch current.

• When analyzing a parallel circuit, remember that the current always has to go somewhere.

• The total current in the circuit is the sum of the currents in all the branches.

• At every branch point the current flowing out must equal the current flowing in.

• This rule is known as Kirchhoff’s current law.

Kirchoff’s Current Law

Kirchoff’s Current Law

Voltage & Current in a Parallel Circuit

• In a parallel circuit the voltage is the same across each branch because each branch has a low resistance path back to the battery.

• The amount of current in each branch in a parallel circuit is not necessarily the same.

• The resistance in each branch determines the current in that branch.

Example #2

• Two bulbs with different resistances are connected in parallel to batteries with a total voltage of 3 volts.

• Calculate the total current supplied by the battery.

Advantages of Parallel Circuits

• Parallel circuits have two big advantages over series circuits:

1. Each device in the circuit sees the full battery voltage.

2. Each device in the circuit may be turned off independently without stopping the current flowing to other devices in the circuit.

Short Circuit

• A short circuit is a parallel path in a circuit with zero or very low resistance.

• Short circuits can be made accidentally by connecting a wire between two other wires at different voltages.

• Short circuits are dangerous because they can draw huge amounts of current.

Resistance in Parallel Circuits

• Adding resistance in parallel provides another path for current, and more current flows.

• When more current flows for the same voltage, the total resistance of the circuit decreases.

• This happens because every new path in a parallel circuit allows more current to flow for the same voltage.

Resistance in Parallel Circuits

Example #3

• A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel.

Calculate the total resistance of the circuit.

Analysis of Circuits

• All circuits work by manipulating currents and voltages.

• The process of circuit analysis means figuring out what the currents and voltages in a circuit are, and also how they are affected by each other.

• Three basic laws are the foundation of circuit analysis.

The 3 Circuit Laws

Solving Circuits Problems

1. Identify what the problem is asking you to find. Assign variables to the unknown quantities.

2. Make a large clear diagram of the circuit. Label all of the known resistances, currents, and voltages. Use the variables you defined to label the unknowns.

3. You may need to combine resistances to find the total circuit resistance. Use multiple steps to combine series and parallel resistors.

Solving Circuits Problems

4. If you know the total resistance and current, use Ohm’s law as V = IR to calculate voltages or voltage drops. If you know the resistance and voltage, use Ohm’s law as I = V ÷ R to calculate the current.

5. An unknown resistance can be found using Ohm’s law as R = V ÷ I, if you know the current and the voltage drop through the resistor.

6. Use Kirchhoff’s current and voltage laws as necessary.

Example #4

• A bulb with a resistance of 1Ω is to be used in a circuit with a 6-volt battery. The bulb requires 1 amp of current. If the bulb were connected directly to the battery, it would draw 6 amps and burn out instantly. To limit the current, a resistor is added in series with the bulb. What size resistor is needed to make the current 1 amp?

Combined Circuits

Key Question:

How do we analyze network circuits?

Combined (Network) Circuits

• In many circuits, resistors are connected both in series and in parallel.

• Such a circuit is called a network circuit.• There is no single formula for adding

resistors in a network circuit.• For very complex circuits, electrical

engineers use computer programs that can rapidly solve equations for the circuit using Kirchhoff’s laws.

Example #5

• Three bulbs, each with a resistance of 3Ω, are combined in the circuit in the diagram

• Three volts are applied to the circuit. • Calculate the current in each of the bulbs. • From your calculations, do you think all three bulbs will

be equally bright?

Electric Power & Energy• The watt (W) is a unit of power.

• Power is the rate at which energy moves or is used.

• Since energy is measured in joules, power is measured in joules per second.

• One joule per second is equal to one watt.• One watt is a pretty small amount of power. • In everyday use, larger units are more convenient

to use. • A kilowatt (kW) is equal to 1,000 watts.

Defining Power

VIPt

VQP

VQtP

VQE

Q

EV

Q

Q

Another Relationship for Power

Example #6

• In North America, the standard electric outlet has a potential difference of 120 V. In Europe, it is 240 V. What would be the power output of a 100W – 120 V light bulb if it was connected to a 240 V system? What would happen to the light bulb?

Example #7

An electric kettle is rated at 1500 W for a 120 V potential difference.

a) What is the resistance of the heating element of the kettle?

b) What will be the power output if the potential difference falls to 108V?

Energy Consumption

• A seemingly unusual unit for energy is used when talking about electrical energy consumption – The kilowatt-hour (KW-h).

• One kilowatt-hour is the energy transformed by 1000 W in one hour (3.6x10^6J).

• A typical charge by an energy company for consumed energy is roughly $0.07 per Kw-h. That means that for 7 cents you can buy enough energy to lift 360 kg a vertical distance of more than 1 km!

Example #8

• A family has its television set on for an average of 4.0 h a day. If the television set is rated at 80 W and energy costs $0.07per Kw-h, how much would it cost to operate the television for 30 days?