Consider the potentiometer circuit arranged as in figure . The potentiometer wire is 600 cm long. If the jockey touches the wire at a distance of 560 cm from A, the current in the galvanometer is I. Find 22I. Take $ε = 1 V a n d r = 1 Ω$ .

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answer is 3.

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Detailed Solution

Resistance per unit length $= \frac{15 r}{6}$
For length $x, R x = \frac{15 r}{6} \times x$
a) For the loop PASQ $(i_{1} + i_{2}) \frac{15}{6} r x + \frac{15}{6} (6 - x) i_{1} + i_{1} R = E$ …….(1)
For the loop AWTM $- i_{2} . R - \frac{15}{6} r x (i_{1} + i_{2}) = E / 2$
$\Rightarrow i_{2} R + \frac{15}{6} r \times (i_{1} + i_{2}) = E / 2$ ………… (2)
For zero deflection galvanometer $i_{2} = 0 \Rightarrow \frac{15}{6} r x . i_{1} = E / 2 = i_{1} = \frac{E}{5 x . r}$
Putting $i_{1} = \frac{E}{5 x . r}$ and $i_{2} = 0$ in equation (1), we get x = 320 cm.
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b) Putting $x = 5.6$ and solving equation (1) and (2) we get $i_{2} = \frac{3 E}{22 r}$