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  • What amount of heat will be generated in a coil of resistance due to a charge passing through it if the current in the coil decreases to zero uniformly during a time interval T?<div class='qna-

What amount of heat will be generated in a coil of resistance due to a charge passing through it if the current in the coil decreases to zero uniformly during a time interval T?

Option: 1

\mathrm{ \frac{4}{3} \frac{q^2 R}{T}}


Option: 2

\mathrm{\ln \left(\frac{q^2 R}{2 T}\right)}


Option: 3

\mathrm{\frac{2 q^2 R}{3 T}}


Option: 4

\mathrm{\ln \left(\frac{2 T}{q^2 R}\right)}


Answers (1)

best_answer

\begin{aligned} &\mathrm{ I=I_0-k t, \text { at } t=T, I=0 \Rightarrow k=I_0 / T }\\ &\mathrm{ \text { So } I=I_0-\frac{I_0 t}{T}, \quad q=\int_0^T I d t=I_0 \int_0^T\left(1-\frac{t}{T}\right) d t }\\ &\mathrm{ \Rightarrow q=\frac{I_0 T}{2} \Rightarrow I_0=\frac{2 q}{T} }\\ &\mathrm{ \text { Heat }=\int_0^T I^2 R d t=I_0^2 R \int_0^T\left(1-\frac{T}{T}\right)^2 d t=\frac{4 q^2 R}{3 T}}\\ \end{aligned}

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Ritika Harsh

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