First slide

Time -Varying current in L-R circuit

Question

An inductor of 2H and a resistance of $10 Ω$ are connected in series with a battery of 5 V. The initial rate of change of current is

Moderate

A

0.5 A/s
B

2.0 A/s
C

2.5 A/s
D

0.25 A/s

Solution

$i = i_{0} (1 - e^{\frac{- Rt}{L}}) \Rightarrow \frac{di}{dt} = \frac{d}{dt} i_{0} - \frac{d}{dt} i_{0} e^{\frac{- Rt}{L}}$
$\Rightarrow \frac{di}{dt} = 0 - i_{0} (- \frac{R}{L}) e^{- \frac{Rt}{L}} = \frac{i_{0} R}{L} e^{- \frac{Rt}{L}}$
Initially, $t = 0 \Rightarrow \frac{di}{dt} = \frac{i_{0} \times R}{L} = \frac{E}{L} = \frac{5}{2} = 2 .5 A / s$

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