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Consider the Potentiometer Circuit as Arranged in the Figure. the Potentiometer Wire is 600 Cm Long. - Physics

Sum

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:-

\[i_2  = \frac{3\epsilon}{22r}\]

  Is there an error in this question or solution?
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 10 Electric Current in Conductors
Q 56 | Page 202
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