Question

A nichrome wire has a resistance of 10 Ω. Find the resistance of another nichrome wire, whose length three times and area of cross-section is four times the first wire.

Answer 1

Case 1: R = 10 Ω

Let \(\text{‘}l\text{’}\) be length and \(\text{‘}a\text{’}\) the area of cross-section.

∴ \[ \text{R} = \rho \frac{l}{a} \]

\[10 = \rho \frac{l}{a} \qquad \text{...(1)} \]

Case 2: \[\text{R}_{1} = ? ; \text {length}=3 l ; \text {area}=4 a\]

∴ \[ \text{R}_{1}=\rho \frac{3 l}{4 a} \]  .....(2)

Dividing (2) by (1)

\[ \frac{R_{1}}{10}=\frac{\rho .3 l}{4 a} \times \frac{a}{\rho . l} \]

∴ \[ \text{R}_{1}=10 \times \frac{3}{4}=7.5 \Omega \]