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  • An inductor-coil of inductance 20 mH having resistance 10 is joined to an ideal battery of emf 5.0 V. What is the

An inductor-coil of inductance 20 mH having resistance 10 \Omega is joined to an ideal battery of emf 5.0 V. What is the rate of change of the induced emf at t = 0:

Option: 1

3.25 \times 10^3 \mathrm{~V} / \mathrm{s}


Option: 2

-2.5 \times 10^3 \mathrm{~V} / \mathrm{s}


Option: 3

4.5 \times 10^3 \mathrm{~V} / \mathrm{s}


Option: 4

-3.5 \times 10^3 \mathrm{~V} / \mathrm{s}


Answers (1)

best_answer

The current after a time t from the instant of closing the key is given as

\mathrm{\begin{aligned} \mathrm{i} & =\frac{\varepsilon}{\mathrm{R}}\left(1-\mathrm{e}^{-\frac{t}{\mathrm{\tau}}}\right) \\ & =\frac{5}{10}\left(1-\mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{\tau}}}\right)=0.5\left(1-\mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{\tau}}}\right) \end{aligned}}

\mathrm{\text { Where } \tau=\frac{\mathrm{L}}{\mathrm{R}}=\frac{20 \times 10^{-3}}{10}=2 \times 10^{-3} \mathrm{~s} \text {. }}

\mathrm{\frac{\mathrm{di}}{\mathrm{dt}}=0.5 \times\left(-\frac{1}{\tau}\right)\left(-\mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{t}}}\right)}

\mathrm{\text { Induced emf. }=\varepsilon \quad=\frac{\text { Ldi }}{\mathrm{dt}}=5 \mathrm{e}^{-\frac{\mathrm{t}}{2 \times 10^{-3}}} \mathrm{volt} / \mathrm{sec} \text {. }}

\mathrm{\left.\therefore \frac{\mathrm{d} \varepsilon}{\mathrm{dt}}\right|_{\mathrm{t}=0}=-2.5 \times 10^3 \text { volt } / \mathrm{sec} .}

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chirag

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