Show that the system shown in Fig. is a double integator. In other words, prove that the transfer gain is given by
$${{{V_0}\,(s)} \over {{V_s}\,(s)}} = - {1 \over {{{(CR\,s)}^2}}}$$, assume ideal OP-Amp

Find the current-transfer-ratio, $${{I_2}}$$/$${{I_1}}$$, for the network shown below (Fig). Also, mark all branch currents.

A series $$R$$-$$L$$-$$C$$ circuit has a $$Q$$ of $$100$$ and an impedance of $$\left( {100 + j0} \right)\,\Omega $$ at its resonant angular frequency of $${10^7}$$ rad/sec. The values of $$R$$ and $$L$$ are: $$R=$$ ______ ohms. $$L=$$ ________Henries.

The current $$i(t)$$ through a $$10$$-$$\Omega $$ resistor in series with an inductance is given by
$$i(t)$$$$ = 3 + 4\sin \left( {100t + {{45}^ \circ }} \right) + 4\sin \left( {300t + {{60}^ \circ }} \right)\,\,A$$.

The RMS value of the current and the power dissipated in the circuit are