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Question
Consider the potentiometer circuit as arranged in the figure. The potentiometer wire is 600 cm long. (a) At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer? (b) If the jockey touches the wire at a distance of 560 cm from A, what will be the current in the galvanometer?
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Solution
Let X be the null point on the wire at a distance x cm from point A, as shown.
Given:-
Total resistance of the wire AB = 15r
Resistance per unit cm = \[\frac{15r}{600}\]
Resistance of x cm of the wire = \[\frac{15rx}{600}\]
Resistance of (600 - x ) cm of the wire = \[\frac{15r\left( 600 - x \right)}{600}\]
(a) Applying KVL in loop 1, we get:-
\[\left( i_1 + i_2 \right)\frac{15}{600}rx + \frac{15}{600}r\left( 600 - x \right) i_1 + i_1 r = \epsilon...........(1)\]
Applying KVL in loop 2, we get:-
\[i_2 r + \frac{15}{600}rx \left( i_1 + i_2 \right) = \frac{\epsilon}{2}............(2)\]
For zero deflection in the galvanometer, i2 = 0. From equation (2),
\[\frac{15}{600}rx\left( i_1 \right) = \frac{\epsilon}{2}\]
\[ \Rightarrow i_1 = \frac{20\epsilon}{rx}\]
Substituting the values of i1 and i2 in equation (1), we get:-
x = 320 cm
(b) Putting x = 560 cm and solving equations (1) and (2), we get:-
\[i_2 = \frac{3\epsilon}{22r}\]
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