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GATE 2026 EE – Question 43

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 2 marks · Multiple choice

The electrical network shown has an independent voltage source (10 V) and a current source (1 u(t) mA).

The voltage across the capacitor at time instants (in seconds) $t=0^+$, $t=0.50$, and $t=\infty$, respectively, is:

Diagram for GATE 2026 EE question 43
  1. 8.00 V, 28.00 V, 26.36 V
  2. 8.00 V, 26.36 V, 28.00 V
  3. 10.00 V, 26.36 V, 28.00 V
  4. 10.00 V, 28.00 V, 26.36 V

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Show answer and explanation

Correct answer: (B) 8.00 V, 26.36 V, 28.00 V

Explanation

Before $t=0$ the capacitor sits at the divider voltage $10\times\dfrac{100}{25+100}=8$ V, and it cannot jump: $v(0^+)=8$ V. For $t>0$ the 1 mA source pushes current into the node. The Thevenin resistance seen by the capacitor is $25\text{ k}\|100\text{ k}=20$ kΩ, so $\tau=20\text{ k}\times10\ \mu\text{F}=0.2$ s, and the final voltage is $8+1\text{ mA}\times20\text{ k}=28$ V. $v(t)=28-20e^{-t/0.2}$, so $v(0.5)=28-20e^{-2.5}=26.36$ V.