Question

Why the potential gradient decreases with increase in resistance?

Answer 1

What does a potentiometer do?

A potentiometer varies the amount of current through an electrical or electronic circuit. It is a instrument used to measure an unknown e.m.f by comparison with known e.m.f. EX: the volume control on your radio is a potentiometer.

Sensitivity of potentiometer: The smallest potential difference that can be measured with the help of Potentiometer. A potentiometer is said to be more sensitive, if it measures a small potential difference more accurately. Sensitivity of potentiometer depends on potential gradient.

Potential Gradient

Potential Gradient is the decrease in potential per unit length. It is calculated as V / L, where V is the potential difference between two points and L is the distance between two points. The longer the wire the lesser the potential gradient and the greater the sensitivity of the potentiometer.

By increasing length of potentiometer wire and by decreasing the potential gradient.

If the potentiometer wire is a fixed length, reducing the current in the circuit by using a rheostat.

Both the methods help in decreasing the potential gradient, and thereby increasing the resistivity.

Principle of Potentiometer

Let us see the principle of potentiometer. In the figure we can have a cell with emf E and internal resistance r, a rheostat and the wire. Consider the length of the wire as L and the resistance of the wire as R. This is the primary circuit of the potentiometer. Now consider the point Q along the wire. So the length of the wire from point P to Q is taken as L(PQ). The principle of potentiometer states that the potential difference between two points across the potentiometer is directly proportional to the length of the corresponding points.

Thus the voltage across the point P and Q,

V(PQ) ∝L(PQ).

To remove the proportionality a constant is called which is the potential gradient. It is denoted as K. So

V(PQ) = K x L(PQ)