Question

An inductor ($L=100mH$), a resistor ($R=100\Omega$ ) and a battery ($E=100V$) are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points A and B. The current in the circuit $1ms$ after the circuit is switched on is

• A. $1A$
• B. $e^{-1}A$
• C. $eA$
• D. $0.1A$

Answer 1

Answer: (B)

$e^{-1}A$

$initiallythecurrentis\frac{E}{R}=1Ai=i_0{e}^{-\left(Rt/l\right)}=e^{\left(\frac{-100t}{0.1}\right)}=e^{-1000t}att=1ms=0.001si=e^{-1}A$