Series and parallel
resistances
pg. 51
Objectives
• Calculate the equivalent
resistance for resistors
connected in both series and
parallel combinations.
• Construct series and parallel
circuits of lamps (resistors).
• Observe and explain relative
lamp brightness in series and
parallel circuits.
Physics terms
• series circuit
• parallel circuit
• equivalent resistance
There are 2 Types of Circuits:
Series Circuit
A series circuit has only
one path for the flow of
electric current.
I
I
Parallel Circuit
In a parallel circuit the
electric current can split
apart and come back
together again.
I
V
V
Impact of Resistors
The battery and the resistors in these circuits are identical.
What is different about these circuits?
I1
I2
I3
The circuit with 3 resistors is 3 times harder for the
current to flow through meaning each of the circuits
has a DIFFERENT amount of current traveling
through it.
Equivalent resistance
Equivalent resistance is the total combined resistance
of a group of resistors.
Think about it, what does equivalent mean?
So if we replaced ALL of the resistors in a circuit with
just 1 resistor, we would still have the same amount of
current going through the circuit because the total
resistance would still be the same.
That 1 resistor had equivalent resistance to all the
original resistors.
Equivalent resistance
These two circuits have the same total resistance . . .
. . . so they will have the same total current, I.
Equivalent resistance: series
For resistors in series, you can find the equivalent
resistance by simply adding up the individual
resistances:
Equivalent Resistance Practice Series
1. A 10 Ω resistor, a 15 Ω resistor, and a 5 Ω resistor are
connected in series. What is the equivalent resistance of this
arrangement? 10 Ω + 15 Ω + 5 Ω = 30 Ω
2. Two strings of tree lights, each with a resistance of 150 Ω,
are connected together in series. What is the Req? 300 Ω
3. When you add resistors in series does Req increase or
decrease? Req increases
4. Does total current increase or decrease when you add
resistors? I decreases
Practice What is the Req of each circuit?
Req = 10 Ω
Req = 15 Ω
Adding resistors in series makes the total resistance
increase.
Practice How much current flows?
I= 1A
I = .67 A
Equivalent resistance: parallel
When you add resistors in parallel, total resistance
goes DOWN.
To find the Req you must add the inverse of the
resistances:
Equivalent resistance: parallel
If you have two 4 Ω resistors in parallel, what is the equivalent
resistance?
A. ½ Ω
B. 2 Ω
C. 4 Ω
D. 8 Ω
Don’t forget to
flip the fraction
at the end!
Parallel circuits
In the circuit with parallel resistors:
total current flow doubles because total resistance is
halved.
What is the Req for the parallel circuit?
R
2R
½R
Equivalent Resistance Practice Parallel
1. A 10 Ω resistor and a 15 Ω resistor are connected in parallel.
What is the Req of this arrangement? 6 ohms
2. Two strings of lights, each with a resistance of 150 Ω, are
connected together. What is the Req when the strings are
connected in parallel? 75 Ω
Practice What is the Req of each circuit?
These are all 10 Ω resistors.
Req = 10 Ω
Req = 5 Ω
Req = 3.3 Ω
Adding resistors in parallel makes the total resistance
decrease.
Practice How much current flows?
I=3A
I= 6A
I=9A
Analogy for resistors in series
What happens to the
potential energy of the
water as it passes through
each water wheel?
How is this analogous
to the voltage drops
across each resistor?
Voltage drops: resistors in series
10 V
drop
20 V
drop
10 V
drop
What are the voltage drops across each resistor in both
circuits?
Voltage drops: resistors in parallel
4A
20 V
drop
20 V
drop
4A
20 V
drop
What are the voltage drops across each resistor in both
circuits?
Calculating total power
What if a circuit contains more than one element?
How do you calculate total power? Here are two ways:
• Find the power of each element separately, and add
them together to get the total power.
OR
•Calculate the total power by multiplying the total current
by the total voltage.
Power for resistors in series
Two 40 Ω resistors are connected in series to a 60-V battery.
a)How much total current flows through the circuit?
b) What is the power output of this circuit?
Power for resistors in parallel
Two 40 Ω resistors are connected in parallel to a 60-V battery.
a)How much total current flows through the circuit?
b) What is the power output of this circuit?
Homes are wired in parallel
Your house is wired in parallel so each appliance will
have 120 volts.
Each device can be turned on and off without affecting the
others.
If you turn off that light bulb, you can still use the computer.
Homes are wired in parallel
What happens when you turn on more appliances?
Because a house is wired in parallel, each additional
appliance draws more current.
Too much current?
Each additional appliance draws more
current from the same outlet.
If the total current exceeds the safety
limit, then a circuit breaker will trip or
a fuse will blow.
To fix the problem:
• Unplug one or more appliances.
• Replace a blown fuse or reset the
circuit breaker by flipping the switch.
Homework
1. Two resistors with resistances of 10 Ω and 30 Ω are connected in
series with a 20 volt battery.
a) What is the equivalent resistance of the circuit?
b) What is the current flow through the circuit?
Homework
2. Two resistors with resistances of 10 Ω and 30 Ω are connected in
parallel with a 20 volt battery.
a) What is the equivalent resistance of the circuit? 7.5 Ω
b) What is the current flow through the circuit?
Homework
3. If you connect these two identical resistors as shown, will they
together draw more or less current than one of the resistors alone?
They will draw more current, because they are connected in
parallel. There are now two different, but identical paths for
electricity to flow, so the current doubles!
Homework
3. Two 30 Ω resistors are connected in series to a 120 volt
outlet.
a) How much current flows through the circuit? 2.0 amps
b) What is the power output of this circuit? 240 watts
Homework
4. Two 30 Ω resistors are connected in parallel to a 120 volt
outlet.
a) How much current flows through the circuit? 8.0 amps
b) What is the power output of this circuit? 980 watts