First slide

Ohm's law

Question

Masses of 3 wires of same metal are in the ratio 1 : 2 : 3 and their lengths are in the ratio 3 : 2 : 1. The electrical resistances are in the ratio

Moderate

A

1 : 4 : 9
B

9 : 4 : 1
C

1 : 2 : 3
D

27 : 6 : 1

Solution

$\begin{array}{l} R \propto \frac{l^{2}}{m} \Rightarrow R_{1} : R_{2} : R_{3} = \frac{l_{1}^{2}}{m_{1}} : \frac{l_{2}^{2}}{m_{2}} : \frac{l_{3}^{2}}{m_{3}} \\ \Rightarrow R_{1} : R_{2} : R_{3} = \frac{9}{1} : \frac{4}{2} : \frac{1}{3} = 27 : 6 : 1 \end{array}$

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