Question

When a potential difference of 2v is applied across the end of a wire of 5 m length a current 1 amp flows through it calculate

(a) the resistance across the ends of the wire if it is doubled on itself

Answer 1

From the given information,

$R=V/I=2\Omega$.
(a) In this case length of wire decreases half of the previous one, but cross sectional area increases two times.

We know, resistance of a wire = $R=\rho \frac{l}{A}$

Let resistance of the wire when it is doubled on itself is R'

or $R^{\prime }=\rho \frac{l/2}{2A}=\rho \frac{l}{4A}=\frac{2}{4}=0.5\Omega$.