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  • A coil of inductance 8.4 mh and resistance 6 is connected to a 12 V battery. The current in the coil is 1.0 A app

A coil of inductance 8.4 mh and resistance 6 \Omega is connected to a 12 V battery. The current in the coil is 1.0 A approximately after time

Option: 1

500 ms


Option: 2

20 s


Option: 3

35 ms


Option: 4

1 ms


Answers (1)

best_answer

\mathrm{\begin{array}{r} L=8.4 \times 10^{-3} \mathrm{H} \\ \mathrm{R}=6 \Omega \\ \mathrm{E}=12 \mathrm{~V} \end{array}}

\mathrm{\therefore \text { Time constant } \tau=\frac{\mathrm{L}}{\mathrm{R}}=\frac{8.4 \times 10^{-3}}{6}=1.4 \times 10^{-3} \mathrm{sec} \text {. }}

\mathrm{\text { For growth of current } i=\frac{E}{R}\left(1-e^{-\frac{R T}{L}}\right)}

\mathrm{\begin{aligned} & 1=\frac{12}{6}\left(1-e^{-\frac{t}{\tau}}\right) \Rightarrow \quad 0.5=1-e^{-t / \tau} \\ & t=-\tau \ln (0.5)=-1.4 \times 10^{-3} \ln (0.5)=1 \mathrm{~ms} \end{aligned}}

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Divya Prakash Singh

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