Question

In the circuit shown in the figure, key K is closed at $t=0$. The current through the key at the instant $t={10}^{-3}\times \ln 2s$ is:

• A. $2A$
• B. $3.5A$
• C. $2.5A$
• D. $0$

Answer 1

The correct option is C $2.5A$

using principle of superposition,
total current thorught key at $t=\ln 2\times {10}^{-3}$ is
$I_{total}=\frac{20}{10}[1-e^{-t/{\tau }_L}]+\frac{20}{10}[1-e^{-t/{\tau }_C}]$
where, ${\tau }_L=L/R$ and ${\tau }_C=CR$

$I_{total}=2.5A$