Question

An inductor of 2 henry and a resistance of 10 ohms are connected in series with a battery of 5 volts. The initial rate of change of current is:

• A. 0.5 amp/sec
• B. 2.0 amp/sec
• C. 2.5 amp/sec
• D. 0.25 amp/sec

Answer 1

The correct option is C 2.5 amp/sec

$i=i_0(1-e^{\frac{-Rt}{l}})$

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

at t=0

$\frac{di}{dt}=\frac{i_0\times R}{l}=\frac{E}{l}=\frac{5}{2}=2.5\frac{amp}{sec}$