GATE 2015 EC – Question 41

Networks, Signals and Systems · Time and Frequency Domain Analysis of Linear Circuits · 2 marks · Numerical answer

In the circuit shown, switch SW is closed at $t = 0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t = 1$ sec is ________.

A 10 V source and a switch SW (closing at $t = 0$) feed a $3\ \Omega$ resistor. Across the output are a $2\ \Omega$ resistor in parallel with a $\frac{5}{6}$ F capacitor, and $v_c(t)$ is the capacitor voltage.

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Correct answer: 2.48 to 2.58

Explanation

Look from the capacitor into the source side. The Thevenin voltage is $10 \times \frac{2}{3 + 2} = 4$ V and the Thevenin resistance is $3 \parallel 2 = 1.2\ \Omega$. The time constant is $1.2 \times \frac{5}{6} = 1$ s. So $v_c(t) = 4(1 - e^{-t})$, and at $t = 1$ s this is $4(1 - 0.368) = 2.53$ V.