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Mixed Combination of Cells

Two wires of ...

Question

Two wires of same mass having ratio of lengths $1 : 2$ , density $1 : 3$ and resistivity $2 : 1$ . These are connected one by one to the same voltage supply. The rate of heat dissipation in the first wire is found to be $10 W$ . Find the rate of heat dissipation in the second wire.

10 W

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\frac{10}{3} W

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5 W

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\frac{5}{3} W

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Solution

The correct option is D $\frac{5}{3} W$
Across a given voltage source, power dissipated in a resistance is given by
$P = \frac{V^{2}}{R}$ For same $V$ ,

$\Rightarrow \frac{P_{1}}{P_{2}} = \frac{R_{2}}{R_{1}} . . . . (1)$

Given that,

$\frac{l_{1}}{l_{2}} = \frac{1}{2}; \frac{d_{1}}{d_{2}} = \frac{1}{3} : \frac{ρ_{1}}{ρ_{2}} = \frac{2}{1}$

and $m_{1} = m_{2}$

$\Rightarrow d_{1} l_{1} A_{1} = d_{2} l_{2} A_{2}$

$\Rightarrow \frac{A_{1}}{A_{2}} = \frac{d_{2} l_{2}}{d_{1} l_{1}} . . . . (2)$

Now, from equations $(1)$ and $(2)$ ,

$\frac{P_{1}}{P_{2}} = \frac{ρ_{2} l_{2} / A_{2}}{ρ_{1} l_{1} / A_{1}} = \frac{ρ_{1} l_{2}}{ρ_{1} l_{1}} \times \frac{A_{1}}{A_{2}}$

$\Rightarrow \frac{P_{1}}{P_{2}} = \frac{ρ_{2} l_{2}^{2} d_{2}}{ρ_{1} l_{1}^{2} d_{1}} = (\frac{1}{2}) \times {(\frac{2}{1})}^{2} \times (\frac{3}{1})$

$\Rightarrow P_{2} = \frac{P_{1}}{6} = \frac{10}{6} = \frac{5}{3} W$

Hence, option $(d)$ is correct answer.

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Mixed Combination of Cells

Standard XII Physics

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Two wires of same mass having ratio of lengths 1:2, density 1:3 and resistivity 2:1. These are connected one by one to the same voltage supply. The rate of heat dissipation in the first wire is found to be 10 W. Find the rate of heat dissipation in the second wire.

Two wires of same mass having ratio of lengths $1 : 2$ , density $1 : 3$ and resistivity $2 : 1$ . These are connected one by one to the same voltage supply. The rate of heat dissipation in the first wire is found to be $10 W$ . Find the rate of heat dissipation in the second wire.