Question

A potentiometer circuit shown in the figure is set up to measure the emf of cell E. As the point P moves from X to Y, the galvanometer G shows the deflection always in one direction, but the deflection decreases continuously until Y is reached. The balance point between X and Y may be obtained by:
                                          

A. Decreasing the resistance R and decreasing V
B. Decreasing the resistance R and increasing V
C. Increasing the resistance R and increasing V
D. Increasing the resistance R and decreasing V

Answer 1

Hint: In this question we have been asked to determine what conditions in the above circuit will balance the point in between X and Y. To solve this question, we will first assume zero deflection in galvanometer i.e. point P is at point Y. We will then find the total current in between point X and Y. later, in the equation obtained we will apply the conditions such that point P moves toward point X.

Complete step-by-step answer:
Now, first let us assume that point P is at point Y and there is no deflection in the galvanometer. The current flowing between point X and Y is say ‘i’.
 Now, let the total resistance between these points be ‘r’.
Therefore, the current i flowing in XY will be given by
$$i={\displaystyle \frac{V}{R+r}}$$ ……………. (Ohm’s law) ………….. (1)
Also, as XY is parallel to emf E, the emf E will be given by
$$E=ir$$ ………… (2)
We need the point P to move towards the point X and obtain a deflection in that direction. To do so, we will have to reduce the resistance r in XY or increase the current flow in XY.
Now from (2)
We can say that to increase the emf E we will have to increase the current flowing in XY assuming r is kept constant.
Also, from (1) it is clear to us that to increase the value of i, either the value of resistance R is to be decreased or the value of is increased. So, decreasing the resistance R or increasing V we can obtain the balance point between X and Y.

So, the correct answer is “Option B”.

Note: A galvanometer is an electromechanical device that is used to detect or indicate the current flowing in a circuit. The galvanometer consists of a solenoid coil. If the current flows through this coil in an anticlockwise direction the galvanometer deflects on the right side. The galvanometer, unlike the ammeter, does not only show the magnitude of current flow but also the direction of the flow of current.