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Adding Resistors to a
Circuit
LearnAid GCSE Physics
Chapter 19 Electrical Circuits
Module 19.2: Adding resistors to a circuit
LearnAid GCSE Physics Chapter 19 Electrical Circuits
Module 19:7 Adding resistors to a circuit
08/05/2017 06:25
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19.7.1
Adding resistors in series and
parallel
Here is a simple circuit –
now lets add some more resistors.
Below are two circuits each
containing three resistors.
In the series circuit the current
is forced through more resistors
– so current decreases.
In the parallel circuit the
current has more paths to
follow – so current increases.
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19.7.2
Resistors in Series Circuits
Consider two resistors in a series circuit with a battery. As you might
expect the total resistance in this circuit is higher than the resistance
of each resistor, because the battery has to push the charge through
both resistors, one after the other. So the total potential difference of
the supply is shared between the components.
R
Total
= R1 + R2
The total resistance in a series circuit is
the sum of the resistances of all the
components.
Also, the voltage is largest across the component with the largest
resistance - because more energy is transferred by the electrons
passing through the large resistance than through the small one.
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Example: Calculating
voltages in a series circuit
19.7.3
Question:
Suppose R1 = 1Ω and R2= 4Ω. If the battery supplies 2.5 Volts what is
the voltage across each resistor?
Answer:
First use the total resistance of the circuit to work out how much
current is flowing through the circuit.
Step 1: Work out the total resistance
a) identify formula: RTotal = R1 + R2
b) insert numbers and units:
RTotal = 1Ω + 4Ω = 5Ω
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Example: Calculating
voltages in a series circuit cont
19.7.3
Step 2: Use Ohm’s Law to calculate the current in the circuit.
a) identify formula (using the triangle)
I = V / R (Ohm’s Law)
b) decide which resistance to use
Use RTotal, so formula becomes I = V / RTotal
c) insert numbers and units: I amps = 2.5V / 5Ω = 0.5A
Now we know how much current is flowing through both resistors,
we can work out the voltage across each resistor
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Example: Calculating
voltages in a series circuit cont
19.7.3
Step 3: Use Ohm’s Law to calculate the voltage across each
resistor.
a) identify formula (using triangle)
V=IxR
b) insert numbers for resistor 1
V1 volts = 0.5A x 1Ω = 0.5 Volts
c) insert numbers for resistor 2
V2 volts = 0.5A x 4Ω = 2.0 Volts
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19.7.3
Potential Dividers
(for higher tier curricula only)
By connecting two resistors in
series we can create what is
called a potential divider.
The two resistors “share” the
total voltage applied across
them, and the bigger resistor
takes the bigger share of the
voltage.
I = V / (R1 + R2) = V1 / R1 = V2 / R2
We can re-arrange this to get:
V2 = V x R2 / (R1 + R2)
This is the potential divider equation, which says that the
voltage across each resistor is shared in the same proportion as the
resistances themselves.
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19.7.3
Potential Dividers
(for higher tier curricula only)
Instead of using two fixed
resistors we can use a
rheostat, or variable resistor.
When wired this way the
rheostat is called a
potentiometer.
When the slider is at 0%, the
voltage Vout is zero. The light
does not shine.
When the slider is at 100% the
ouput voltage Vout is equal to
the fixed input voltage Vin. The
lamp shines at its brightest.
At positions between 0% and 100% the
voltage Vout is somewhere in between.
We can rewrite the potential divider
equation as follows:
Vout = Vin x R2 / (R1 + R2)
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19.7.4
Resistors in Parallel Circuits
When several components are connected in
parallel branches, the voltage
(potential difference) across each
parallel branch is the same. And this is
the same as the voltage across the battery.
Total current flowing through the
battery is the sum of the currents
flowing through each branch.
IMain = I1 + I2
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19.7.4
Resistors in Parallel Circuits cont
Because there are more paths for the charge to flow along,
the total resistance is less than either of the two
paths on their own. And therefore (with the same
battery) the current is bigger.
To find out the resistance of the whole circuit , we can’t
just add together the resistors as we did in the series
circuit. We have to apply Ohm’s Law ( I = V / R ) to
each branch of the circuit.
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19.7.5 Example: Calculating the resistance of
several resistors in parallel
Question:
Suppose R1 = 2Ω and R2= 1Ω. If the battery supplies 2.5 Volts what is
the combined resistance of the circuit?
Answer:
Step 1: Use Ohm’s Law to calculate the current in each branch
the circuit, as if the other branch did not exist.
a) identify formula (using the triangle) I1 = V / R1 (Ohm’s Law)
b) insert numbers and units I1 amps = 2.5V / 2Ω = 1.25A
c) identify formula (using the triangle) I2 = V / R2 (Ohm’s Law)
d) insert numbers and units I2 amps = 2.5V / 1Ω = 2.5A
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Calculating the resistance
of several resistors in parallel cont
19.7.5 Example:
Step 2: Add the currents together, and calculate the total
current in the main branch.
a) identify formula IMain = I1 + I2
b) insert numbers and units IMain amps = 1.25 amps + 2.5 amps =
3.75 amps
Step 3: Use Ohm’s Law to calculate the resistance of the total
circuit.
d) identify formula (using triangle): RTotal = V / IMain
e) insert numbers and units RTotal Ω = 2.5V / 3.75 amps = 0.67 Ω
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19.7.6 Example 2: Calculating the resistance of
several resistors in parallel – using the
formula
This is 1/ RTotal = 1/ R1 + 1/ R2
Question:
Suppose R1 = 2Ω and R2 = 1Ω. If the battery supplies 1.5 Volts what
is the combined resistance of the circuit?
Answer:
Step 1: Use Ohm’s Law to calculate the current in each branch
the circuit.
h) identify formula 1/ RTotal = 1/ R1 + 1/ R2
i) insert numbers 1/ RTotal = 1/ 2 + 1/ 1 = 3/ 2
So: RTotal = 2/ 3 Ω = 0.67 Ω
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19.7.7
Key Points for Revision:
Series circuits

all components are part of the same electrical loop, and the
current through each component is the same

voltage is shared across all the components, and is larger across
components with higher resistance

the sum of voltage across all the components equal the voltage
across the battery

resistors in series have more resistance than each resistor on its
own
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19.7.7
Key Points for Revision:
Series circuits cont

the total resistance is the sum of the resistance of each
component

the current through two or more resistors in series is lower than if
each resistor were on its own;

(higher tier only) the output voltage from a potential divider is
calculated from the input voltage multiplied by the share of the
resistance in the output section of the circuit.
The equation is : Vout = Vin x R2 / (R1 + R2)
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19.7.7
Key Points for Revision:
parallel circuits

in parallel circuits there are several branches after the battery

the voltage across each branch is the same, and equals the
voltage of the battery;

the current in each branch is the same as if it were the only
branch in the circuit; apply Ohm’s Law to each branch separately;
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19.7.7
Key Points for Revision:
parallel circuits cont

the current through the whole circuit (and the battery) is the sum
of the currents through each branch;

the current is largest through the branch with the lowest
resistance

the resistance of two or more resistors in parallel is lower than
each resistor on its own (because there are more paths to follow)
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LearnAid GCSE Physics Chapter 19 Electrical Circuits
Module 19:2 Circuits and Current
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LearnAid GCSE Physics Chapter 19 Electrical Circuits
Module 19:2 Circuits and Current
08/05/20
17 06:25
19