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P6B
Resistors in series
Two or more resistors in a circuit increase
the circuit’s resistance.
When components are connected in
series, their total resistance is the sum of
their individual resistances:
RT = R1 + R2 + R3
Where:
The potential divider
A potential divider is used to produce the
required voltage in a circuit.
Two fixed resistors can be used as a
potential divider.
In the circuit diagram for a potential
divider:

the two resistors are shown as R1 and
R2
 RT is the total resistance
 R1, R2 and R3 are the individual
resistances

the input voltage is shown as Vin

the output voltage is shown as Vout
Note that it does not matter how many
components are connected in series.
For example, the total resistance of two 5
Ω (ohm) resistors in series is 10 Ω (5 Ω + 5
Ω).
The total resistance given by these three
resistors is 2 + 1 + 3 = 6 Ω
If you increase the number of lamps in a
series circuit, the total resistance will
increase and less current will flow.
The output voltage depends on the
relative resistances of the two resistors.
For example:

if the resistance of R1 and R2 is the
same, Vout is ½ of Vin

if the resistance of R2 is double the
resistance of R1, Vout is ⅔ of Vin

if the resistance of R2 is three times
the resistance of R1, Vout is ¾ of Vin

One of the fixed resistors can be
replaced by a variable resistor. This
produces a potential divider that
allows the output voltage to be varied,
even if the input voltage stays the
same.
LDRs and thermistors
You should be able to recognise the circuit
symbols for the thermistor and the LDR
(light-dependent resistor), and know how
the resistance of these components can
be changed.
The thermistor
Thermistors are used as temperature
sensors, for example, in fire alarms. Their
resistance decreases as the temperature
increases:

at low temperatures, the resistance
of a thermistor is high - and little
current can flow through it
Take care not to confuse the symbol for a
thermistor with the symbol for a variable
resistor (which contains an arrow rather
than a bent line).
The LDR
LDRs (light-dependent resistors) are used
to detect light levels, for example, in
automatic security lights. Their resistance
decreases as the light intensity increases:

in the dark and at low light levels, the
resistance of an LDR is high - and little
current can flow through it

in bright light, the resistance of an
LDR is low - and more current can
flow through it
LDRs are also useful for controlling how
long the shutter should remain open on a
digital camera.
Changes in the resistance are measured
and, if the light level is low, the shutter
stays open for longer than if the light level
is high.
Resistors in parallel
The equation below shows how to
calculate the total resistance for three
resistors in parallel:
1/R = 1/R + 1/R + 1/R
T
1
2
3
For example, what is the total resistance
when three 6 Ω resistors are connected in
parallel?
1/R
T

at high temperatures, the resistance
of a thermistor is low - and more
current can flow through it
= 1/6 + 1/6 + 1/6 = 1/R3
The value of 1/RT = 1/2, so the value of RT
is 2 Ω.
Remember that when components are
connected in series, their total resistance
is the sum of their individual resistances
(RT = R1 + R2 + R3).
There are two general points to note:

Vout is approximately the same as Vin
when R2 is much greater than R1
Therefore if these three 6 Ω resistors were
connected in series, the total resistance
would be 6 + 6 + 6 = 18 Ω

Vout is approximately zero when R1 is
much greater than R2
The potential divider
You need to be able to calculate the value
of Vout if you are given the values of Vin, R1
and R2 for a potential divider.
You can calculate Vout using this equation:
Vout = R2 / R1 + R2 x Vin
For example, what is the output voltage
when the input voltage is 12 V, R1 = 2 Ω
and R2 is 1 Ω?
Vout = 1/ 2 + 1 x 12 = 1/ 3 x 12 = 4 Ω
The fixed resistor R2 can be replaced by a
thermistor or an LDR. If a thermistor is
used, Vout depends on the temperature. If
a thermistor is used, Vout depends on the
light levels.