In an $A.C.$ circuit,the instantaneous $e.m.f.$ and current are given by:
$e = 100 \sin(20t)$
$i = 20 \sin(30t - \frac{\pi}{4})$
In one cycle of $A.C.$,the average power consumed by the circuit and the wattless current are,respectively:

$A$ coil has inductance of $0.4 \text{ H}$ and resistance of $8 \Omega$. It is connected to an $AC$ source with peak emf $4 \text{ V}$ and frequency $\frac{30}{\pi} \text{ Hz}$. The average power dissipated in the circuit is (in $\text{ W}$)

$A$ $ 100 \,W $ bulb is connected to an $ AC $ source of $ 220 \,V, 50 \,Hz $. Then the current flowing through the bulb is

In the shown $AC$ circuit,the phase difference between currents $I_1$ and $I_2$ is:

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $e.m.f$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

Find the peak current and resonant frequency of the following circuit (as shown in the figure).