Question

In the circuit shown if switch S is closed at $t=0$, then $i_1$ and $i_2$ be the current at any finite time $t$. The ratio $\frac{\left(i_1\right)}{\left(i_2\right)}$ is

• A. is constant
• B. increases with time
• C. decreases with time
• D. first increases and then decreases

Answer 1

The correct option is C

decreases with time

From the given situation we have,

$i_1=\frac{V}{R}\left(e^{-t/RC}\right)$ and $i_2=\frac{V}{R}\left(e^{-t/3RC}\right)$

$\frac{i_1}{i_2}=e^{\frac{-2t}{3RC}}$ which decrease with time