$A$ sinusoidal alternating current of peak value $I_0$ passes through a heater of resistance $R$. What is the mean power output of the heater?

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:

$A$ sinusoidal $AC$ current passes through a resistor of resistance $R$ in an $LCR$ series circuit. If the phase difference between the supplied voltage and the supplied current is $\theta$ and the peak value of the supplied current is $I_0$,then the power dissipated in the circuit is:

Assertion $(A):$ If the frequency of the applied $AC$ is doubled,then the power factor of a series $R-L$ circuit decreases.
Reason $(R):$ Power factor of series $R-L$ circuit is given by $\cos \theta = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$.

$A$ series $LCR$ circuit is connected to an $AC$ source of voltage $V = 150 \sin(80 \pi t) \text{ V}$. If the resistance of the resistor in the circuit is $25 \ \Omega$ and the impedance in the circuit is $75 \ \Omega$, the average power dissipated per cycle in the circuit is: (in $\text{ W}$)

An e.m.f. $e=E_0 \cos \omega t$ is applied to a circuit containing $L, C$ and $R$ in series where $X_L=3 R$ and $X_C=R$. The average power dissipated in the circuit is