Question

A nichrome wire of length L and area of cross section A/4 has a resistance R. Another nichrome wire of length 3L and area of cross section A/2 has a resistance of R1, find the ratio of R1: R

Answer 1

$$\begin{gathered} R=\rho \frac{l}{A} \\ forthefirstwire, \\ R=\rho \frac{L}{A/4} \\ =4\rho \frac{L}{A} \\ Forthesecondwire, \\ R1=\rho \frac{3L}{A/2} \\ =6\rho \frac{L}{A} \\ \frac{R1}{R}=\frac{6}{4}=\frac{2}{3} \end{gathered}$$