GATE EC 2014 Set 2 — Question 42
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Network Theory → Transient & AC Analysis → RL, RC & RLC Transients
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Question
In the figure shown (, , ), the capacitor is initially uncharged. Which one of the following expressions describes the current (in mA) through for ?
Correct answer
(A) I(t) = (5)/(3) (1 - e^(-t/τ)), τ = (2)/(3) msec
Solution
Here , , , and is the current through , which equals .Initial value. The capacitor is uncharged, so and .Final value. In steady state the capacitor is open:Time constant. With the source shorted, the capacitor sees :Therefore mA with ms. Options (B) and (D) use the wrong final current ( mA would need alone across 5 V), and (C) and (D) use the wrong time constant (3 ms would be ).Answer: (A)
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