In a series LR circuit, $$X_L=R$$, power factor is $$P_1$$. If a capacitor of capacitance $$C$$ with $$X_C=X_L$$ is added to the circuit the power factor becomes $$P_2$$. The ratio of $$P_1$$ to $$P_2$$ will be

An e.m.f. $$E=4 \cos (1000 t)$$ volt is applied to an LR circuit of inductance $$3 \mathrm{~mH}$$ and resistance $$4 ~\Omega$$. The maximum current in the circuit is

An alternating voltage of frequency '$$\omega$$' is induced in electric circuit consisting of an inductance '$$L$$' and capacitance '$$C$$', connected in parallel. Then across the inductance coil

The reactance of capacitor at $$50 \mathrm{~Hz}$$ is $$5 \Omega$$. If the frequency is increased to $$100 \mathrm{~Hz}$$, the new reactance is