Electricity &

Magnetism UnitUnderstanding Circuits

Objectives1. Recognize and sketch examples of series and parallel

circuits.2. Describe a short circuit and why a short circuit may be

a dangerous hazard.3. Calculate the current in a series or parallel circuit

containing up to three resistances.4. Calculate the total resistance of a circuit by combining

series or parallel resistances.5. Describe the differences between AC and DC electricity.6. Calculate the power used in an AC or DC circuit from

the current and voltage.

Chapter 20 Vocabulary Terms

series circuit parallel circuit short circuit network circuit circuit analysis power Kirchhoff’s voltage

law voltage drop direct current (DC)

alternating current (AC)

kilowatt Kirchhoff’s current

law horsepower power factor circuit breaker watt kilowatt-hour

20.1 Series and Parallel CircuitsKey Question:How do series and parallel circuits work?

*Students read Section 20.1 AFTER Investigation 20.1

20.1 Series and Parallel Circuits• In series circuits, current can only take one path.• The amount of current is the same at all points in a

series circuit.

20.1 Adding resistances in series

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

Rtotal = R1 + R2 + R3...Total

resistance(ohms)

Individual resistances (W)

20.1 Total resistance in a series circuit

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

20.1 Calculate current

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

20.1 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.

20.1 Series and 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.

20.1 Series and 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.

20.1 Voltage and 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.

20.1 Advantages of parallel circuitsParallel 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.

20.1 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.

20.1 Calculate current

• 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.

20.1 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.

20.1 Adding resistance in parallel circuits

• A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel. • Calculate the total resistance of the circuit.

20.2 Solving circuit problems1. 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.

20.2 Solving circuit problems4. 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.

20.2 Solving circuit problems• 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?

20.2 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.

20.2 Calculate using network circuits

• 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?

20.3 Electric Power, AC, and DC Electricity• 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.

20.3 Reviewing terms

20.3 Power in electric circuits

• 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.• The other common unit of power often seen on

electric motors is the horsepower.• One horsepower is 746 watts.

20.3 Power

P = VI Current (amps)Voltage (volts)

Power (watts)

20.3 Calculate power

• A light bulb with a resistance of 1.5Ω is connected to a 1.5-volt battery in the circuit shown at right. • Calculate the power

used by the light bulb.

20.3 Paying for electricity• Electric companies charge for the

number of kilowatt-hours used during a set period of time, often a month.• One kilowatt-hour (kWh) means

that a kilowatt of power has been used for one hour. • Since power multiplied by time is

energy, a kilowatt-hour is a unit of energy. • One kilowatt-hour is 3.6 x 106

joules.

20.3 Calculate power

• Your electric company charges 14 cents per kilowatt-hour. Your coffee maker has a power rating of 1,050 watts. • How much does it cost to use the coffee maker one

hour per day for a month?

20.3 Alternating and direct current• The current from a battery is

always in the same direction. • One end of the battery is

positive and the other end is negative. • The direction of current flows

from positive to negative. • This is called direct current,

or DC.

20.3 Alternating and direct current• If voltage alternates, so does

current.• When the voltage is positive,

the current in the circuit is clockwise.• When the voltage is negative

the current is the opposite direction. • This type of current is called

alternating current, or AC.

20.3 Alternating and direct current• AC current is used for almost all high-power

applications because it is easier to generate and to transmit over long distances.• The 120 volt AC (VAC) electricity used in homes and

businesses alternates between peak values of +170 V and -170 V at a frequency of 60 Hz.• AC electricity is usually identified by the average

voltage, (120 VAC) not the peak voltage.

20.3 Power in AC circuits• For a circuit containing a

motor, the power calculation is a little different from that for a simple resistance like a light bulb. • Because motors store energy

and act like generators, the current and voltage are not in phase with each other.• The current is always a little

behind the voltage.

20.3 Power for AC circuits• Electrical engineers use a power factor (pf) to calculate power

for AC circuits with motors

P = VI x pf

Avg. current (amps)Avg. voltage (volts)

Power (watts)

power factor0-100%

Application: Wiring in Homes and Buildings

Application: Wiring in Homes and Buildings