The switch in the circuit in the figure is in position $P$ for a long time and then moved to position $Q$ at time $t=0$

The value of $\frac{d v(t)}{d t}$ at $t=0^{+}$is

The switch has been in position 1for a long time and abruptly changes to position 2 at t = 0. If time t is in seconds, the capacitor voltage V_C (in volts) for t>0 is given by

In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The energy (in $$\mu J$$) taken from the 3V source to charge the 0.1$$\mu$$F capacitor from 0V to 3V is

A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage V_S, the resistance R, the capacitance C, and the current i(t) is given below: $$$V_{s\;}=\;Ri(t)+\frac1c\int_0^ti(u)du$$$ Which one of the following represents the current f(t)?