First slide

Ohm's law

Question

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

Easy

A

1 : 3 : 5
B

5 : 3 : 1
C

1 : 15 : 125
D

125 : 15 : 1

Solution

$R = \frac{ρ l}{A} = \frac{ρ l^{2}}{A l} = \frac{ρ l^{2}}{V} = \frac{ρ l^{2}}{m / d} = \frac{ρ d l^{2}}{m} o r R \propto \frac{l^{2}}{m}$
$R_{1} : R_{2} : R_{3} = \frac{l_{1}^{2}}{m_{1}} : \frac{l_{2}^{2}}{m_{2}} : \frac{l_{3}^{2}}{m_{3}} = \frac{25}{1} : \frac{9}{3} : \frac{1}{5} = 125 : 15 : 1$

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