N ATIONAL 5 P HYSICS
E LECTRICITY AND
E NERGY
V OLTAGE D IVIDER
S UPPLEMENT The Potential Divider aka The Voltage Divider
1
1
1
=
+
+ ..
RT
R1 R2
A potential divider provides a convenient way of obtaining a variable voltage from a
fixed voltage supply.
Consider two fixed resistors, R1 and R2, connected in series across a supply with voltage
Vs, as shown below:
R1
Vs
V1
R2
V2 =
Vs
R1 + R2
R2
V2
The current in the two resistors will be the same, however the voltage across the two
resistors will be split. Whilst we could use Ohm’s Law to calculate V1 and V2 (Or R1 and
R2) there are two ‘shortcut’ formulae we can use. Both are on the formula sheet. The
first, given below, is useful when you know 3 out of the 4 variables:
V1 R1
=
V2 R2
P = IV
=
RT
R1
+
R2
+ ...
The second is useful when you know the supply voltage and the value of both resistors
but not V1 or V2. This is a very handy formula that can save you much time when
solving potential divider questions. It is given below:
R2
V2 =
Vs
R1 + R2
V1 R1
=
V2 R2
Example
3Ω
V1
5Ω
V2
6V
P = IV
Find the values of V1 and V2
P= I R
2
Application
Voltage dividers can be connected to a transistor. By switching one of the resistors for
another component (such as an LDR) allows the construction of an automatic switching
circuit as shown below:
This circuit works as following:
• As the light level falls the resistance across the LDR increases.
• As the resistance of the LDR increases the voltage across the LDR increases.
• Once the voltage across the LDR reaches the switching voltage of the transistor the
transistor will with on.
• When the transistor switches on the LED will light up.
Practice Problems
A high intensity LED is used as a garden light. The light turns on automatically when it
is dark. The light also contains a solar cell which charges a rechargeable battery during
daylight hours.
Part of the circuit is shown below:
At a particular light level the voltage generated by the solar cell is 1.5 V. Calculate the
voltage across the rechargeable battery at this light level
3
The LED is switched on using the following circuit:
Name component X
1
Explain how this circuit is able to switch the LED on when the light level falls.
3
A thermistor is used as a temperature sensor in a circuit to monitor and control the
temperature of water in a tank. Part of the circuit is shown.
The variable resistor R is set at a resistance of 1050 Ω. Calculate the resistance of the
thermistor when the voltage across the thermistor is 2·0 V.
4
The graph shows how the resistance of the thermistor varies with temperature.
Use the graph to determine the temperature of the water when the voltage across the
thermistor is 2·0 V.
1
The circuit is now connected to a switching circuit to operate a heater.
Explain how the circuit operates to switch on the heater when the temperature falls
below a certain value.
3
The resistance of the variable resistor R is now increased. What effect does this have on
the temperature at which the heater is switched on? You must justify your answer.
3