Question

An inductor of 2 H and a resistance of 100 are connected in series with a battery of 5 V. The initial rate of change of current is

• A. 0.5 A/s
• B. 2.0 A/s
• C. 2.5 A/s
• D. 0.25 A/s

Answer 1

Answer: (C)

2.5 A/s

$i=i_{o}1-e^{-\frac{Rt}{L}}$

$\to \frac{di}{dt}=\frac{d}{dt}{i}_0{e}^{-\frac{Rt}{L}}=0+\frac{i_{0}R}{L}{e}^{\frac{Rt}{L}}$

Initially, $t=0$
$\Rightarrow \frac{di}{dt}=\frac{i_0\times R}{L}=\frac{E}{L}=\frac{5}{2}=2.5A/s$