The masses of the three wires of copper are in the ratio $5 : 3 : 1$ and their lengths are in the ratio $1 : 3 : 5$ . The ratio of their electrical resistance is?

5 : 3 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{125} : 15 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 15 : 125

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 : 3 : 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $1 : 15 : 125$
Given $l_{1} = 1 k, l_{2} = 3 k, l_{3} = 5 k$
and $m_{1} = 5 m, m_{2} = 3 m, m_{3} = 1 m$

Resistance R $= \frac{ρ l}{A}$
$ρ$ is the resistivity of the material of the conductor.

So, $R_{1} : R_{2} : R_{3} = \frac{l_{1}}{A_{1}} : \frac{l_{2}}{A_{2}} : \frac{l_{3}}{A_{3}}$

$= \frac{l_{1}^{2}}{V_{1}} : \frac{l_{2}^{2}}{V_{2}} : \frac{l_{3}^{2}}{V_{3}}$

$= \frac{l_{1}^{2}}{m_{1}} : \frac{l_{2}^{2}}{m_{2}} : \frac{l_{3}^{2}}{m_{3}}$

$= \frac{1}{5} : \frac{9}{3} : \frac{25}{1}$

$= 1 : 15 : 125$ .

Suggest Corrections

Similar questions

The masses of three wires of copper are in the ratio of 1:3:5 and their lengths are in the ratio 5:3:1. The ratio of their electrical resistance is :

1 : 3 : 5

5 : 3 : 1

The mass of the three wire of copper are in the ratio 1:3:5, and their lengths are in ratio 5:3:1. The ratio of their electrical resistance is

Join BYJU'S Learning Program