An inductor of $\left(\frac{100}{\pi}\right) \mathrm{mH}$, capacitor of capacitance $\left(\frac{10^{-3}}{2 \pi}\right) \mathrm{F}$ and resistance of $10 \Omega$ are connected in series with an AC voltage source of $110 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The tangent of the phase angle ' $\phi$ ' between voltage and current is

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

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)