Question

Given a wire of resistance R Ω. The resistance of a wire of the same material and same weight and double the diameter is ___________

(a) 0.5 R

(b) 0.25 R

(c) 0.125 R

(d) 0.0625 R

The question was asked during an online exam.

The question is from Advanced Problems on Network Theorems topic in chapter Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Right answer is (d) 0.0625 R

For explanation: Since diameter is double, area of cross-section is four times and length is one-fourth.

It can be verified by the following equation,

R2 = \(\frac{\frac{ρl}{4}}{4A}\)

= \(\frac{ρl}{16 A} = \frac{R}{16}\).