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20.1 Series and Parallel
In series circuits, current can only take one path.
The amount of current is the same at all points in a series
20.1 Adding resistances in
Each resistance in a series circuit
adds to the total resistance of the
Rtotal = R1 + R2 + R3...
Total resistance
Individual resistances (W)
20.1 Series and Parallel
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.
Voltage and Current in a Parallel
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
1. Each device in the circuit sees the full battery
2. Each device in the circuit may be turned off
independently without stopping the current
flowing to other devices in the circuit.
20.1 Adding resistance in parallel
A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel.
Calculate the total resistance of the circuit.
20.2 Three circuit laws
20.2 Voltage divider
A circuit divides any supplied voltage by a ratio of the resistors.
V0 =
R1 + R2
resistor ratio
20.2 Solving circuit
Identify what the problem is asking you to find. Assign variables
to the unknown quantities.
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.
You may need to combine resistances to find the total circuit
resistance. Use multiple steps to combine series and parallel
20.3 Alternating and
direct current
The current from a battery
is always in the same
One end of the battery is
positive and the other end
is negative.
The direction of current
flows from positive to
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.
20.2 Solving circuit
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.
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.
Use Kirchhoff’s current and voltage laws as necessary.
20.2 Solving circuit
A bulb with a resistance of 1Ω is to
be used in a circuit with a 6-volt
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
Such a circuit is called a network circuit.
There is no single formula for adding resistors in a network
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
 Three volts are applied to the
 Calculate the current in each
of the bulbs.
 From your calculations, do
you think all three bulbs will
be equally bright?
20.3 Power
Voltage (volts)
Power (watts)
P = VI
Current (amps)
20.3 Calculate power
A light bulb with a
resistance of 3Ω is
connected to a 1.5volt 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
 Since power multiplied by time
is energy, a kilowatt-hour is a
unit of energy.
 One kilowatt-hour is 3.6 x 106
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
AC current is used for almost all high-power applications
because it is easier to generate and to transmit over long
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.
Application: Wiring in Homes and
Application: Wiring in Homes and