First slide

Time -Varying current in L-R circuit

Question

An inductor of 5 henry and a resistance of 10 ohms are connected in series with a battery of 15 volts. The initial rate of change of current is

Moderate

A

3.5 amp/sec
B

2.0 amp/sec
C

3.0 amp/sec
D

0.25 amp/sec

Solution

$i = i_{0} (1 - e^{\frac{- Rt}{L}}) \Rightarrow \frac{di}{dt} = \frac{d}{dt} i_{0} - \frac{d}{dt} i_{0} e^{\frac{- Rt}{L}}$
$\Rightarrow \frac{di}{dt} = 0 - i_{0} (- \frac{R}{L}) e^{- \frac{Rt}{L}} = \frac{i_{0} R}{L} e^{- \frac{Rt}{L}}$
$Initially, t = 0 \Rightarrow \frac{di}{dt} = \frac{i_{0} \times R}{L} = \frac{E}{L} = \frac{15}{5} = 3 amp / \sec .$

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