First slide

Time -Varying current in L-R circuit

Question

The resistance and inductance of series circuit are $5 Ω$ and 20 H, respectively. At the instant of closing the switch, the current is increasing at the rate 4 A/s. The supply voltage is

Moderate

A

20 V
B

80 V
C

120 V
D

100 V

Solution

$i = i_{0} (1 - e^{- \frac{Rt}{L}}) \Rightarrow \frac{di}{dt} = - i_{0} (- \frac{R}{L}) e^{- \frac{Rt}{L}} = \frac{i_{0} R}{L} \cdot e^{- \frac{Rt}{L}}$
$At t = 0, \frac{di}{dt} = \frac{i_{0} R}{L} = \frac{E}{L} \Rightarrow 4 = \frac{E}{20} \Rightarrow E = 80 V$

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