Q. The resistance and inductance of series circuit are $5\Omega$ and $20H$ respectively. At the instant of closing the switch, the current is increasing at the rate $4A/s$. The supply voltage is
A) $20\ V$
B) $80\ V$
C) $120\ V$
D) $100\ V$
Explanation
(b) $i = i_{0}\left( 1 - e^{\frac{Rt}{L}} \right) \Rightarrow \frac{di}{dt} = - i_{0}\left( - \frac{R}{L} \right)e^{\frac{Rt}{L}} = \frac{i_{0}R}{L}.e^{\frac{Rt}{L}}$
At $t = 0;\frac{di}{dt} = \frac{i_{0}R}{L} = \frac{E}{L} \Rightarrow 4 = \frac{E}{20} \Rightarrow E = 80\ V$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.