Question

In the given circuit diagram key $K$ is switched on at $t=0.$ The ratio of current $i$ through the cell at $t=0$ to that at $t=\infty$ will be

• A. $3:1$
• B. $1:3$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is A $3:1$

AT $t=0,$ the branch containing L will offer infinite resistance while the branch containing the capacitor will be effectively a short circuit.Hence,$(i{)}_t=0=\frac{\epsilon }{R}$.Similarly at $t=\infty ,L$ will be offer zero resistance whereas C will be open circuit.Hence

effective resistance $=R+\frac{6\times 3R}{6+3}=3R(i{)}_{t=\infty }=\frac{\epsilon }{3R}$

The required ratio $=\frac{\epsilon }{R}\times \frac{3R}{\epsilon }=3:1$