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Question

The figure shows a potentiometer of total resistance RT with a sliding contact.

The resistance between the points P and Q of the potentiometer at the position of the contact shown is RC and the voltage ratio V0/Vs at this point is 0.5. If the ratio RL/RT=1, the ratio RC/RT is

A
1+52
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B
1+52
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C
1+5
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D
1+5
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Solution

The correct option is A 1+52

Given,
RLRT=1

RL=RT

Also,

Vs2=(RTRC)Is=(RT||RC)Is

using (i),

RTRC=RC.RTRC+RT

R2TR2C=RCRT

RTRCRCRT=1

Let RCRT=x

1xx=1

x2+x1=0

x=1±52

Since,
x=RCRT>0

RCRT=512

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