JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Current Electricity

A wire of resistance

R_{1}

is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is:

Answer: (A)

Solution

When a wire is drawn out, its volume remains constant. If length increases from

L_{1}

3 L_{1}

(increased by twice the original), then area decreases from

A_{1}

A_{1} /3

. Resistance

R = ρ \frac{L}{A}

. Original:

R_{1} = ρ \frac{L _{1}}{A _{1}}

. New:

R_{2} = ρ \frac{3 L _{1}}{A _{1} /3} = 9 ρ \frac{L _{1}}{A _{1}} = 9 R_{1}

. Ratio

R_{2} : R_{1} = 9 : 1

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Single correct option