Question

the length of the potentiometer wire is l. a cell of emf e is balanced at length l/3 from the positive end of the wire. if the length of the wire is increased by l/2, at what distance will the same cell give a balance point

Answer 1

Potential gradient in the first case = E₀l

E=l/3 E₀l E₀3

In the second case =2E₀/3l/2

E=(X) 2E₀3l/2

On solving these two equations,

we get x=l/2

Answer 2

Given:

Length of the potentiometer wire = l.

EMF E is balanced at length = $\frac {l} {3}$ from the positive end of the wire

Increase in the length = $\frac {1} {2}$

Potential gradient in 1st case = $\frac {E} {l}$….(1)

Potential gradient in 2nd case can be written as= $\farc {2E_0} {3 \frac {l} {2}}$ …(2)

From equation 1 and 2;

                                            $x = \frac{l}{ 2}$