4.3.3 Potential dividers

Potential divider circuits can vary the p.d. across an output (e.g a lamp) when connected to a fixed point. These are useful in circumstances such as having a 10V battery but only needing 6V for the task you are about to perform.

Basically, there are two resistors in a series circuit. All you have to do is connect a circuit across one of these resistors. The p.d. into this circuit (which is Vout of the potential divider circuit) can be varied from zero to maximum depending on the resistances of R1 and R2.

This  means that the p.d. across each resistor in a potential divider depends on the resistances of the individual resistors...

V1/V2 = R1/R2

We can determine Vout by the potential divider equation:

Vout = (R2/(R1+R2)) x Vin

You can also 'load' a potential divider circuit. This refers to adding an additional resistor/component to the Vout part in parallel which overall decreases the total resistance of this part which lowers Vout. A small additional resistance in parallel significantly reduces Vout.

The potentiometer
To vary Vout we can replace one of the fixed resistors with a variable resistor. A potentiometer is a type of variable resistor that has 3 terminals and a sliding contact. If you adjust the contact the p.d. between two of the terminals will vary. Potentiometers are very compact which is useful so they can be used for portable electronic devices etc.

Temperature sensing circuits
To vary Vout we can replace one of the fixed resistors with a variable resistor.

Replacing the variable resistor with a fixed resistor allows Vout to vary depending on the temperature of the surroundings (as temperature increases resistance of the thermistor decreases as thermistors have a negative temperature coefficient).

Light sensing circuits
A similar principle to temperature sensing circuits only replace the variable resistor with an LDR. As light intensity increases, resistance falls.

4.3.2 Internal resistance

It is important to understand that different power sources have different internal resistances. E.g if a large current is needed, a power supply with a small internal resistance is used. If a small current is needed, a power supply with a large internal resistance is used.

So, what is internal resistance? Basically, when there is a current in a power source work has to be done by the charges to move through the power source. The p.d. measured at the terminals of the power source (the terminal p.d.) is always less than the actual emf (provided there is a current in the circuit) - the difference is the lost volts.

From K2 we can determine this equation:

electromotive force (emf) = p.d. + lost volts

It is important to realise that changing the current will change the lost volts and consequently the terminal p.d.. An increase in the current means that more charges travel through the cell each second meaning overall more work is done by the charges. This increases the lost volts which subsequently reduces the terminal p.d.

We can apply V=IR to lost volts too (lost volts = Ir, where r is the internal resistance). This means that total emf is equal to IR + Ir...

emf = I(R+r)

We also need to be able to determine the internal resistance of a cell/source of emf:

• Create a series circuit with a variable resistor
• Introduce a voltmeter across a power supply
• Have an ammeter in the circuit (it doesn't matter where as it is a series circuit)
• Change the resistance of the circuit - this will draw different currents from the power source.
• Rearrange E= V+Ir to give V = -Ir + E
• Plot a graph of V against I
• The gradient will be -r, the y intercept will be the emf

4.3.1 series and parallel circuits

Kirchoff's Laws
Kirchoff's first law states that the sum of currents into a point always equals the sum of currents out of a point. This is conservation of charge.
Kirchoff's second law states that the sum of the emfs is equal to the sum of the pds around a closed loop. This is conservation of energy.

During GCSE you will have come across series and parallel circuits (I hope!). Here is a reminder...

A series circuit has only one path for current. From K1 we can deduce that, since charge is not used up, the rate of flow of charge is the same at all points in the circuit. Since current is the rate of flow of charge this means current is the same at all points in the circuit. From K2 we know that the emf is shared between each component as there is only one closed loop. Adding additional components in series reduces the emf that is shared between the original components. We know that V=IR and I is constant (in series circuits). The total V = V1+V2... this means that the total resistance (R)= R1+R2...

A parallel circuit has more than one possible path for current. The resistance of each path determines how much current will flow down it. The greater the resistance, the lower the current that passes down it (V=IR and V is constant). Each branch of a parallel circuit forms it's own loop. from K2 we can deduce that the pd around each individual loop is equal to the emf from the power supply. In parallel circuits, V is constant. This means that I/V=I1/V+I2/V..... I/V = 1/R. This means that 1/R = 1/R1+1/R2...

These rules can be used to create a circuit with a required resistance.


When using more than one emf source, we must look at which polarity the emfs are in. We need to think about the internal resistance when combining emf sources in series and parallel.

In series: the emf will change but resistance will be constant

In parallel: the emf will be constant but resistance will change

Image source: Kerboodle OCR A Physics textbook p183