The relation between the input current $(I)$ and the output voltage $(V)$ of a circuit is governed by the equation: $C \frac{d V}{d t}=I(t)-m(t)$. The circuit is excited by $I(t)=q \delta(t)$, where $q$ is a real valued constant. V at $t=0^{-}$is $V_0$.

Which of the following is an equivalent representation of the above case?

The output voltage $V_o$ (in Volt) for the network given in the Figure is $\_\_\_\_$ . (rounded off to two decimal places)

Consider the circuit shown in the Figure, where the input $v_i(t)$ is in Volt.

The average power (in mW ) dissipated in the load resistance of $1 \mathrm{k} \Omega$ at the resonant frequency is $\_\_\_\_$ .

(rounded off to two decimal places)

In the given circuit, $L=1 \mu \mathrm{H}$ and $C=1 \mu \mathrm{~F}$. The phasor diagram for $I_C$ and $I_L$ is also shown. Assume that the phase $\left(\theta_1+\theta_2\right)$ is $90^{\circ}$ at a frequency of 159.15 kHz . Among the following options, what is the nearest integer value of $R_C \times R_L$ ?