A potentiometer consists of a long uniform wire generally made of managing or constantan stretched on a wooden board.(sometimes there are four of more wires each one meter long fixed parallel to one another and connected in series by thick copper strips) its ends are connected to the binding screws A and B. A metre scale is fixed on the board parallel to the length of the wire. The potentiometer is provided with a jockey j with the help of which the contact can be made at any point on the wire. A battery E (called driving cell), connected across A and B sends the current through the wire which is kept constant by using a rheostat Rh.
The working of a potentiometer is based on the fact that the fall of potential across any portion of the wire is directly proportional to the length of that portion provided the wire is of uniform area of cross section and a constant current is flowing through it.
Suppose A and p are the area of cross – section and specific resistance of the material of the wire let v be the potential difference across the portion of the wire of length whose resistance is R. if I is the current flowing through the wire, then from Ohm’ law: V = IR
∴ V = Ip I / A = KA, (where K = Ip/A)
(∴ R = pt/A)
Or V ∝ I (if I and A are constant)
Where V / I = K potential gradient the fall of potential per unit length of wire.
A current of 1.0 mA is flowing through a potentiometer wire of length 4 m and of resistance 4 Ω find the potential gradient of potentiometer wire.
Here ; I = 1.0 mA = 10-3 A;
R = 4 Ω; L = 4 m
Potential drop across potentiometer wire,
V = IR = 10-3 x 4 V
K = V / L = 4 x 10-3 / 4 = 10-3 V/m
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