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Logic Gates

In the circui...

Question

In the circuit shown, key (K) is closed at $t = 0$ . Current through key at $t = 10^{- 3} l n (2)$ is

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Solution

$i_{1} = 2 (1 - e^{\frac{- R_{2} t}{L}}) \Rightarrow R_{2} = 10 Ω$

$q = C ε (1 - e^{\frac{- t}{R_{1} C}}) \Rightarrow R_{1} = 10 Ω$

$i_{2} = \frac{ε}{R_{1}} e^{\frac{- t}{R_{1} C}}$ $\frac{L}{R_{2}} = 10^{- 3}$

$i = i_{1} + i_{2} = 2 (1 - e^{- l n 2}) + 2 e^{- l n (2)}$

$i = 2 A$

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