Q. 56

# Consider the potentiometer circuit arranged as in 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?

Answer :

Concepts/Formula used:

Ohm’s Law:

Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:

Let the area of cross section of the wire (resistor) be A and resistivity be ρ.

Then,

Kirchhoff’s loop rule:

The sum of potential differences around a closed loop is zero.

(a)

We consider the circuit when there is no deflection:

Applying Kirchhoff’s rule on loop ABCF,

Using ,

Let the area of cross section of wire be A and resistivity be ρ.

Then,

where V is the voltage across a wire segment of length l.

As, all the quantities except for length are the same for all sections of wire AB,

Hence,

(b)

Let the current coming out of the main battery be I_{1} and the current through the galvanometer be I_{2}.

Let the area of cross section of wire be A and resistivity be ρ.

Then,

where V is the voltage across a wire segment of length l.

As, all the quantities except for length are the same for all sections of wire AB,

Hence,

Using

Now, R_{AD} and R_{DB} are in series.

Applying Kirchhoff’s rule on loop ABCFA,

……………(1)

Applying Kirchhoff’s rule on loop ADEFA,

………………(2)

From (i) and (ii)

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