GATE ECE 2004 | Transient Response Question 31 | Network Theory

The circuit shown in Fig, has initial current $${\mathrm i}_\mathrm L\left(0^-\right)\;=\;1\;\mathrm A$$ through the inductor and an initial voltage $${\mathrm v}_\mathrm C\left(0^-\right)\;=\;-1\;\mathrm V$$ across the capacitor. For input v(t) = u(t), the Laplace transform of the current i(t) for t ≥ 0 is

GATE ECE 2004 Network Theory - Transient Response Question 31 English

$$\frac s{s^2\;+\;s\;+\;1}$$

$$\frac{s\;+\;2}{s^2\;+\;s\;+\;1}$$

$$\frac{s\;-\;1}{s^2\;+\;s\;+\;1}$$

$$\frac{s\;+\;1}{s^2\;+\;s\;+\;1}$$

GATE ECE 2003

MCQ (Single Correct Answer)

-0.6

The circuit is given in figure.Assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

GATE ECE 2003 Network Theory - Transient Response Question 35 English

At t = 0⁺, the current i₁ is

$$\frac{-\mathrm V}{2\mathrm R}$$

$$\frac{-\mathrm V}{\mathrm R}$$

$$\frac{-\mathrm V}{4\mathrm R}$$

zero

GATE ECE 2003

MCQ (Single Correct Answer)

-0.6

The circuit is given in figure.Assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

GATE ECE 2003 Network Theory - Transient Response Question 34 English

I₁(s) and I₂(s) are the Laplace transforms of i₁(t) and i₂(t) respectively. The equations for the loop currents I₁(s) and I₂(s) for the circuit shown in figure, after the switch is brought from position 1 to position 2 at t = 0, are