Question

A resistance of R Ω draws current from a potentiometer, as shown in the figure. The potentiometer has a total resistance Ro Ω. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

Answer 1

The voltage across R when the sliding contact is in the middle of the potentio-meter is V' = 2 VR / Ro + 4 R

Explanation:

• The resistance of the parallel combination of R and R0/2.
• The equivalent resistance between A and C.

1/R1 = 1/R + 1 /Ro /2

On solving , We get

R1 = RRo / 2R + Ro

• The equivalent resistance of the circuit becomes.

R' = Ro / 2 + RRo / 2R + Ro

R' = (2RRo +Ro^2 + 2Rro) / 2 (2R + Ro)

R' = 4 RRo + Ro^2 / 2 (2R + Ro)

The net current in the circuit is.

I net = V / R'

Voltage across R is

V ' = Inet x R1 = V / R' x R1 = V /  4 RRo + Ro^2 / 2 (2R + Ro) x RRo / 2R + Ro

V' = 2 VR / Ro + 4 R

Thus the voltage across R when the sliding contact is in the middle of the potentio-meter is V' = 2 VR / Ro + 4 R