Protection Resistor

In practice, the potentiometer circuit can be more complicated. For example, a protection resistor *R*_{2} may be added in series with *E*_{2}. This is to limit the magnitude of the current *i* while we are still searching for the null deflection. However, having *R*_{2} does not complicate our calculation of *E*_{2} at all. This is because at null deflection, *V*_{CD} is still equal to *E*_{2}. This is because at null deflection, no current is flowing through *R*_{2} so the PD across *R*_{2} is zero.

Protection Resistor

Similarly, the internal resistance of *E*_{2} does not complicate our measurement of *E*_{2} at all. Again, this is because at null deflection, *V*_{CD} is still equal to *E*_{2}. This is because at null deflection, no current is flowing through *r* so the PD across *r* is zero.

Precision Resistor

We also often include a resistor *R*_{1} in the driver circuit. By the Potential Divider Principle, if the total resistance of the slide wire is *R _{w}*, then

The calculation of *E*_{2} is now going to be

Having *R*_{1} reduces *V*_{AB}. While this decreases the range of voltages the potentiometer can balance, it has the benefit of a longer balance length AX. A smaller percentage uncertainty in the measurement of AX ultimately results in a more precise measurement of *E*_{2}.

Adding a Secondary Circuit

The diagram below shows a potentiometer being used to measure not just the EMF, but terminal PD *V*_{t} of cell *E*_{2} at different loading. (Can’t they just use the voltmeter? Sigh)

Notice *E*_{2} now has a complete circuit of its own called the secondary circuit. So there is a current *I*_{3} running through the internal resistance *r* even at null deflection. This means that *V*_{CD} is no longer equal to *E*_{2} even at null deflection (unless *R*_{3} is infinitely large)

However, since there is no current flowing between driver and secondary circuit at null deflection, we can still analyse the two circuits separately, as if they are not connected to each other.

For the driver circuit, we have

For the secondary circuit, we have

*V*_{CD} is still equal to *V*_{AB}, so *E*_{2} can be calculated through

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**Video Explanation**

Adding Resistors and Secondary Circuit

**Concept Test**