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  • A battery of 10 volt is connected to a resistance of 20 ohm through a variable resistance R. The amount of charge which has passed in the circuit in 4 minutes, if the variable resistance R is incre

A battery of 10 volt is connected to a resistance of 20 ohm through a variable resistance R. The amount of charge which has passed in the circuit in 4 minutes, if the variable resistance R is increased at the rate of 5 ohm/min.

Option: 1

120 \; coulomb


Option: 2

120 \log _{\mathrm{e}} 2 \: coulomb


Option: 3

\frac{120}{\log _e 2}\: coulomb


Option: 4

\frac{60}{\log _e 2}\: coulomb


Answers (1)

best_answer

\begin{aligned} & \mathrm{I}=\frac{\mathrm{dq}}{\mathrm{dt}}=\frac{\mathrm{V}}{\mathrm{R}} \\ & \frac{\mathrm{dq}}{\mathrm{dR}} \cdot \frac{\mathrm{dR}}{\mathrm{dt}}=\frac{\mathrm{V}}{\mathrm{R}} \\ & \mathrm{dq}=12 \mathrm{~V} \frac{\mathrm{dR}}{\mathrm{R}} \\ & \mathrm{q}=12 \mathrm{~V} \int_{20}^{40} \frac{\mathrm{dR}}{\mathrm{R}}=12 \mathrm{~V}\left(\log _{\mathrm{e}} 40-\log _{\mathrm{e}} 20\right) \end{aligned}

=12 \times 10 \times \log _e 2

Posted by

Ritika Kankaria

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