A coil with a quality factor $$(Q)$$ of $$10$$ is put in series with a capacitor $${C_1}$$ of $$10\,\,\mu F,$$ and the combination is found to draw maximum current when a sinusoidal voltage of frequency $$50$$ $$Hz$$ is applied. A second capacitor $${C_2}$$ is now in parallel with the circuit. What should be the capacitance of $${C_2}$$ for combined circuit to act purely as a resistance for a sinusoidal excitation at a frequency of $$100$$ $$Hz$$? Calculate the rms current drawn by the combined circuit at $$100$$ $$Hz$$ if the applied voltage is $$100V$$ (rms).

A 2-port network is shown in figure. The parameter $${h_{21}}$$ for this network can be given by

A modulated signal is given by s(t)= $${e^{ - at}}$$ cos $$\left[ {({\omega _c} + \Delta \omega )t} \right]$$ u (t), where a, $${\omega _c}$$ and $${\Delta \omega }$$ are positive constants, and $${\omega _c}$$ >>$${\Delta \omega }$$. The complex envelope of s(t) is given by

A signal x(t) has a Fourier transform X ($$\omega $$). If x(t) is a real and odd function of t, then X($$\omega $$) is