In the following circuit the capacitance varies as C = KQ, where K is a constant equal to 0.5 Farads/Coulomb and Q, the charge on the capacitor in Coulombs. Determine the current through the circuit and sketch the voltage waveform across the capacitor (V_C) for a step input V_i as shown in figure.

The network shown in figure is initially under steady-state condition with the switch in position 1. The switch is moved from position 1 to position 2 at t = 0. Calculate the current i(t) through R₁ after switching.