$A$ capacitor of $\frac{2.5}{\pi} \mu F$ and a resistor of $3000 \, \Omega$ are connected in series with a $200 \, V, 50 \, Hz$ $AC$ source. What are the power factor and the power dissipated,respectively?

$A$ resistor of $450 \Omega$ and an inductor are connected in series to an ac source of frequency $\frac{75}{\pi} \text{ Hz}$. If the power factor of the circuit is $0.6$,then the inductance connected in the circuit is:

If $i$ is the current in an $L-C-R$ series $AC$ circuit,what are the formulas for:
$(i)$ Voltage across resistance.
$(ii)$ Voltage across inductor.
$(iii)$ Voltage across capacitor.

An ideal inductor of $\left(\frac{1}{\pi}\right) H$ is connected in series with a $300 \Omega$ resistor. If a $20 \ V, 200 \ Hz$ alternating source is connected across the combination,the phase difference between the voltage and current is

In a series $LR$ circuit,$X_L=R$,the 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

$A$ coil having an inductance of $\frac{1}{\pi} \text{ H}$ is connected in series with a resistance of $300 \text{ } \Omega$. If $20 \text{ V}$ from a $200 \text{ Hz}$ source are impressed across the combination,the value of the phase angle between the voltage and the current is