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Q.

The resistance and inductance of series circuit are $5 Ω$ and 20H, respectively. At the instant of closing the switch, the current is increasing at the rate $4 {As}^{- 1}$ . The supply voltage is___________V

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answer is 80.

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Detailed Solution

For growth of current in L-R circuit, current is given by $i = i_{0} (1 - e^{Rt / L})$
$∴ \frac{di}{dt} = - i_{0} (- \frac{R}{L}) e^{Rt / L} = \frac{i_{0} R}{L} e^{- Rt / L}$ , At the instant of closing the switch, $\frac{di}{dt} = \frac{i_{0} R}{L} = \frac{E}{L}$
$\Rightarrow 4 = \frac{E}{20} ∴ E = 20 \times 4 = 80 V$

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