The switch in the circuit shown was on position ‘a’ for a long time and is moved to position ‘b’ at time t = 0. The current i(t) for t > 0 is given by

The time domain behavior of an RL circuit is represented by $$$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm{dt}}+\mathrm{Ri}\;=\;{\mathrm V}_0\left(1\;+\;\mathrm{Be}^{-\mathrm{Rt}/\mathrm L}\;\sin\;\mathrm t\right)\mathrm u\left(\mathrm t\right)$$$ For an initial current of i(0) = $$\frac{{\mathrm V}_0}{\mathrm R}$$, the steady state value of the current is given by

The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the output voltage V_c(t) is

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage V_c(t) across the capacitor is given by