The power factor of a good choke coil is

An inductor $20 \, mH$,a capacitor $100 \, \mu F$ and a resistor $50 \, \Omega$ are connected in series across a source of emf,$V = 10 \sin(314 \, t)$. The power loss in the circuit is ...... $W$.

In an $A.C.$ circuit,the $e.m.f.$ $(\varepsilon)$ and the current $(i)$ at any instant are given respectively by $E = E_o \sin \omega t$ and $i = I_o \sin(\omega t - \phi)$. The average power in the circuit over one cycle of $A.C.$ is:

$(a)$ For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.
$(b)$ Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Explain.

In an $AC$ circuit,the voltage and current are described by $V = 200 \sin(314t - \frac{\pi}{6}) \text{ V}$ and $i = 50 \sin(314t + \frac{\pi}{6}) \text{ mA}$ respectively. The average power dissipated in the circuit is $...... \text{ W}$.

The power factor of an $R-L$ circuit is $\frac{1}{\sqrt{3}}$. If the inductive reactance is $2 \Omega$,the value of the resistance is: