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

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.

At t = 0⁺, the current i₁ is

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.

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

The voltage V_C1, V_C2 and V_C3 across the capacitors in the circuit in Fig., under steady state, are respectively