Electricity
&
Magnetism Unit
Understanding Circuits
Objectives
1. 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
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series circuit
parallel circuit
short circuit
network circuit
circuit analysis
power
Kirchhoff’s voltage law
voltage drop direct
current (DC)
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alternating current (AC)
kilowatt
Kirchhoff’s current law
horsepower
power factor
circuit breaker
watt
kilowatt-hour
20.1 Series and Parallel Circuits
Key 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 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.
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 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.
20.2 Solving circuit 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.
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
Voltage (volts)
Power (watts)
P = VI
Current (amps)
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
Avg. voltage
(volts)
Power (watts)
Avg. current (amps)
P = VI x pf
power factor
0-100%
Application: Wiring in Homes and
Buildings
Application: Wiring in Homes and
Buildings