Consider a DC voltage source connected to a series R-C circuit. When the steady-state reaches, the ratio of the energy stored in the capacitor to the total energy supplied by the voltage source, is equal to

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

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.

A series LCR circuit consisting of $$R = 10\Omega $$, $$\left| {{X_L}} \right|\,\,\, = 20\Omega $$ and $$\left| {{X_C}} \right|\,\,\, = 20\Omega $$, is connected across an a.c. supply of $$200V$$ rms. The rms voltage across the capacitor is