In the circuit as shown in figure, the switch is closed at t = 0. The current through the capacitor will decrease exponentially with a time constant of magnitude

In the circuit as shown in figure, the switch is closed at t = 0. The current through the capacitor will decrease exponentially with a time constant of magnitude Correct Answer 1 s

Concept:

Time constant of a circuit is the time taken to rise the 63.2% of input voltage.

Time constant of R-L circuit (τ) = L/R

Time constant of R-C circuit (τ) = RC

Calculation:

After t = 0, the circuit diagram becomes as shown below

[ alt="F1 U.B. Nita 29.10.2019 D29" src="//storage.googleapis.com/tb-img/production/19/10/F1_U.B._Nita_29.10.2019_D29.png" style="width: 207px; height: 128px;">

Equivalent resistance (R) is the equivalent resistance across capacitor terminals by replacing all the independent voltage sources with short circuit and all the independent current sources with open circuit.

Now, the circuit becomes as shown below

[ alt="F1 U.B. Nita 29.10.2019 D28" src="//storage.googleapis.com/tb-img/production/19/10/F1_U.B._Nita_29.10.2019_D28.png" style="width: 180px; height: 132px;">

Now, equivalent resistance (R) = 1 Ω

Capacitance (C) = 1 F

Time constant (τ) = RC = 1 s

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