Question

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

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

Answer 1

The correct option is C $2.5A/s$

$i=i_0[1-e^{-\frac{Rt}{L}}]$
$\Rightarrow \frac{di}{dt}=\frac{d}{dt}{i}_0-\frac{d}{dt}\left[i_0{e}^{-\frac{Rt}{L}}\right]=0+-\frac{R}{L}{i}_0{e}^{-\frac{Rt}{L}}$
Initially $t=0$
$\Rightarrow \frac{di}{dt}=\frac{i_0\times R}{L}=\frac{E}{L}=\frac{5}{2}=2.5A/s$.