CBSE Class 12 · 2017 · Delhi · Current ElectricityShort Answer

A resistance

R

draws current from a potentiometer whose wire AB has total resistance

R_{0}

; a voltage

V

is supplied to the potentiometer. Derive an expression for the voltage across

R

when the sliding contact is at the middle of the wire.

Answer: $V_{R} = \frac{2 R V}{R _{0} + 4 R}$ .

Solution

With the slider at the middle, the lower half

\frac{R _{0}}{2}

is in parallel with the load

R

R_{∥} = \frac{R ( R _{0} /2 )}{R + R _{0} /2}

. This is in series with the upper half

\frac{R _{0}}{2}

across

V

. The current drawn is

I = \frac{V}{R _{∥} + R _{0} /2}

, and the voltage across

R

works out to

V_{R} = I R_{∥} = \frac{2 R V}{R _{0} + 4 R} .

CBSE Class 12 Board · 2017 · Delhi · Subjective