A potentiometer wire PQ is made by using two wires of different cross sectional area A and 2A as shown. The material of wire PS and SQ is same and their lengths are 5m each. An ideal source battery of 10V is connected in the circuit. Choose the correct option(s) regarding the balance point.

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If an ideal cell of emf $e_{0} = 5 V$ is used, then balance point from the end P is at 3.75 m

If an ideal cell of emf $e_{0} = 8 V$ is used, then balance point from the end P is at 7m

If an ideal cell of emf $e_{0} = 8 V$ is used, then balance point from the end P is at 8.5m

Balance point is independent of internal resistance of the cell.

answer is A, B, D.

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Detailed Solution

Current in the circuit $i = \frac{10}{R + \frac{R}{2}} = \frac{20}{3 R}$
$\Rightarrow$ Potential drop across $P S = i R = \frac{20}{3} V$
Potential drop across $S Q = i (\frac{R}{2}) = \frac{10}{3} V$
Potential q radiant for $P S = \frac{20 / 3}{5} = \frac{4}{3} V$
$\Rightarrow$ Potential q radiant for $S Q = \frac{10 / 3}{5} = \frac{2}{3} V$
Length required for $5 V = \frac{5}{4 / 3} V = 3.75 m$
$\Rightarrow$ Length required for $8 V = 5 + \frac{8 - \frac{20}{3}}{2 / 3} = 7 m$