$$ \text { The frequency at resonance for the circuit is } $$

In an a.c. circuit containing $L, C, R$ in series the ratio of true power to apparent power is ( $\mathrm{Z}=$ impedance of the circuit and R is the resistance)

In series LCR circuit R $=18 \Omega$ and impedance is $30 \Omega$. An rms voltage 210 V is applied across the circuit. The true power consumed in AC circuit is nearly

A resistor of $5 . \Omega$, inductor of self inductance $\left(\frac{2}{\pi^2}\right) \mathrm{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. When the voltage and current are in phase, the value of capacitance is