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

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If a cell of emf e₀=8V is used, then balance point from the end P is at 8.57 m

If a cell of emf e₀=5V is used, then balance point from the end P is at 7.5 m

If a cell of emf e₀=8V is used, then balance point from the end P is at 7 m

If a cell of emf e₀=5V is used, then balance point from the end P is at 3.75 m

answer is B, C.

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Detailed Solution

Current in the circut
$i = \frac{5}{R + \frac{R}{2}} = \frac{20}{3 R} \Rightarrow$ Potential drop across PS $= iR = \frac{20}{30} V$
Potential drop across SQ $= i (\frac{R}{2}) = \frac{10}{3} V$
$\Rightarrow$ Potential q radiant for PS $= \frac{20 / 3}{5} = \frac{4}{3} V / m$
Potential q radian for SQ $= \frac{10 / 3}{5} = \frac{2}{3} V / m$
$\Rightarrow$ Length required for 5V $= \frac{5}{4 / 3} V = 3.75 m$
Length required for 8V $= 5 + \frac{8 - \frac{20}{3}}{2 / 3} = 7 m$