The vector diagram of current and voltage for a circuit is as shown. The components of the circuit will be

$A$ resistor $R=300 \Omega$ and a capacitor $C=25 \mu F$ are connected in series with a $50 \ V, \frac{50}{\pi} \ Hz$ $AC$ source. The average power dissipated in the circuit is (in $W$)

An electrical device draws $2 \, kW$ power from $AC$ mains $(V_{rms} = 223 \, V = \sqrt{50000} \, V)$. The current lags in phase by $\tan \phi = -\frac{3}{4}$ compared to the voltage. Find $(i)$ $R$,$(ii)$ $X_C - X_L$,and $(iii)$ $I_M$. Another device has twice the values for $R$,$X_C$,and $X_L$. How are the answers affected?

Given below are two statements $:$ one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A) :$ Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube,the tube will be damaged.
Reason $(R):$ By using the choke coil,the voltage across the tube is reduced by a factor $\left(R / \sqrt{R^2+\omega^2 L^2}\right)$,where $\omega$ is the angular frequency of the supply,$R$ is the resistance,and $L$ is the inductance. If the choke coil were not used,the voltage across the tube would be the same as the applied voltage. In the light of the above statements,choose the most appropriate answer from the options given below $:$

$L$,$C$,and $R$ represent the physical quantities inductance,capacitance,and resistance,respectively. Which of the following combinations has the dimensions of frequency?

$A$ $\frac{2.5}{\pi} \mu F$ capacitor and $3000 \, \Omega$ resistor are joined in series to an $AC$ source of $200 \, V$ and $50 \, Hz$ frequency. The power factor of the circuit and the power dissipated in it will respectively be: