Question

the given figure, the potentiometer wire AB has a resistance of $5\Omega $ and length 10m. The balancing length AJ for the emf 0.4V is

A: 8m
B: 0.8m
C: 4m
D: 0.4m

Answer 1

Hint: In this circuit, we are given a potentiometer and we are expected to find its balancing length. We have not noted the point that for any potentiometer, the current flowing through the galvanometer will be zero at its balancing point. Hence we can easily find the potential drop from the given conditions.

Step by step answer:
Ohm’s law is used here.
If V is the velocity, I is the current and R is the resistance then $V=IR$
We’re given the resistance of AB=$5\Omega $
And the length of AB= $10m$

We know that the current flowing through the galvanometer will be zero at the balancing point.
Hence, the potential drop across AJ will balance the 0.4V.
Hence, ${{V}_{AJ}}=0.4V$
To find potential across AB,
$I=\dfrac{5}{45+5}=\dfrac{5}{50}=\dfrac{1}{10}A$
We know that $V=IR$
Hence,
$V=\dfrac{1}{10}\times 5=0.5V$
We are given that the length of AB is 10m
We have derived that AB drops a voltage of 0.5V
 1V is dropped by $\dfrac{10}{0.5}units$
0.4V is dropped by $\dfrac{10}{0.5}\times 0.4=8 units$

Hence the required balancing length or AJ will be 8m.

Therefore, option A is the correct answer among the given options.

Note: Potentiometers are very accurate as their working is based on the comparative method rather than the deflective method. It can also measure the balance point or the null point that doesn’t need the power for measurement. There is no source resistance as the current doesn’t flow at the point of balance.