Question

The potentiometer consists of a wire of length $4\,m$ and resistance $ 10\,\Omega. $ It is connected to a cell of emf $2V$ the potential difference per unit length of the wire will be :

• A. 10 V/m
• B. 5 V/m
• C. 2 V/m
• D. 0.5 V/m

Answer 1

Answer: (D)

Potential difference across any portion of the wire.is proportional to the length of that portion.
We know that
voltage $=$ current $\times$ resistance
$\therefore i=\frac{E}{R}$
$=\frac{2}{10}=0.2 \,A$
From the principle of potentiometer when a constant current is passed through a wire of uniform cross-section the potential difference across any portion of the wire is directly proportional to the length of that portion i.e.,
$V=k L$
So, potential difference per unit length of the wire, i.e., potential gradient
$k =\frac{V}{l} $
$\therefore =\frac{i R}{l} =\frac{0.2 \times 10}{4}$
$=0.5\, V / m.$