# The potential divider

The basic circuit is shown in the first circuit diagram. The output voltage across AB is given by :

Output voltage (V2) = (R2/[R1 + R2])V

Note that the input voltage (V) in this case supplied by the battery is constant. The current flowing through both resistors is the same (series circuit) and so the output voltage across one of them depends simply on the two resistance values and the input voltage.

(V = IR1 + IR2 and V2 = IR2 and so V2/V = R2/[R1+R2])

## Measuring the output

If we now attempt to actually MEASURE the output voltage things may change.

(a) Firstly consider using a digital voltmeter with very high (if not virtually infinite) resistance (RV). The resistor R2 and the voltmeter are connected in parallel and so their combined resistance (R) is given by the equation;

1/R = 1/R2 +1/RV

but as we have said, RV is huge – almost infinite and so 1/RV is virtually 0 and can be ignored.
This means that 1/R = 1/R2 and so R = R2.

The output voltage (Vo) measured by the meter really is that across R2, in other words V2.

(b) A moving coil meter. These meters have a much lower resistance than a digital meter, usually some tens of kΩ. This means that the combined resistance of R2 and RV is affected by the resistance of the voltmeter and is actually lower than R2. (Connecting two resistors in parallel gives a resulting resistance lower than either resistor).

The proportion of the input voltage (V) dropped across R2 therefore falls and so the output voltage (Vo) is less than that measured with a digital meter.

## Replacing R2 with a Light dependent resistor (LDR)

The LDR is a component that has a resistance that changes when light falls on it. As the intensity of the light is increased so the resistance of the LDR falls.

If the LDR is connected as part of a potential divider as shown in the diagram then as the light level is increased its resistance falls and the proportion of the input voltage dropped across it will also fall.

So in the light V2 is low and in the dark V2 is high.

## Replacing R2 with a thermistor

Something very similar happens if R2 is replaced by a thermistor. As the temperature of the thermistor rises its resistance falls and so the voltage dropped across it falls.

When the thermistor is hot V2 is low and when the thermistor is cold V2 is high.

Of course both these examples have considered R2 being replaced by another component. If R1 is replaced then if the voltage across this component rises the output voltage across R2 will fall. (The total voltage across both the resistor and the other component in the circuit must always stay the same and be equal to the supply voltage of the battery.)

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