| A 20 Henry inductor and coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rated of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is: |
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A) \[\frac{1}{2}\ell n2\]
B) \[\ell n2\]
C) \[2\ell n2\]
D) \[\frac{2}{\ell n2}\]
Correct Answer: C
Solution :
\[{{i}^{2}}R=\left( \tau \frac{di}{dt} \right)i\] \[\Rightarrow \] \[iR=\tau \frac{di}{dt}\] \[\Rightarrow \] \[\frac{di}{dt}=\frac{i}{\tau }\] \[{{e}^{-\,t/\tau }}=1-{{e}^{-t/\tau }}\] \[\Rightarrow \] \[2{{e}^{-t/\tau }}=1\] \[\Rightarrow \] \[t=\tau \ell n2\] \[\tau =\frac{\tau }{R}=\frac{20}{10}=2\] \[t=2\ell n2.\]
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