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GATE 2016 EC (EC2) – Question 17

Networks, Signals and Systems · Time and Frequency Domain Analysis of Linear Circuits · 1 mark · Multiple choice

The switch has been in position 1 for a long time and changes abruptly to position 2 at $t=0$. With t in seconds, the capacitor voltage $V_C$ in volts for $t>0$ is

Diagram for GATE 2016 EC (EC2) question 17
  1. $4(1-e^{-t/0.5})$
  2. $10-6e^{-t/0.5}$
  3. $4(1-e^{-t/0.6})$
  4. $10-6e^{-t/0.6}$

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Correct answer: (D) $10-6e^{-t/0.6}$

Explanation

Before switching, the capacitor is open at DC. The 3 Ω/2 Ω divider gives $V_C(0^-)=10(2)/(3+2)=4$ V, and capacitor voltage is continuous.

After switching, the final open-circuit capacitor voltage is $5\cdot2=10$ V. Suppress the independent current source to find the resistance seen by C: 4+2=6 Ω. Thus $\tau=6(0.1)=0.6$ s.

The first-order response is $10+(4-10)e^{-t/0.6}$, giving **D**.

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