A periodic voltage wave from has been shown in fig. Determine the average value of voltage (in $V$).

The source voltage and current in the circuit are represented by the following equations $E=110 \sin \left(\omega t+\frac{\pi }{6}\right) \mathrm{volt}, I=5\sin \left(\omega t-\frac{\pi }{6}\right) \mathrm{ampere}$.

Find Impedance of circuit (in ohm).

When an alternating voltage of $220 \mathrm{V}$ is applied across a device $X$, a current of $0.5 \mathrm{A}$ flows through the circuit and is phase with the applied voltage. When the same voltage is applied across another device $Y$, the same current again flows through the circuit but it leads the applied voltage by $\frac{\pi }{2}$ radians.

Calculate the current (in ampere) flowing in the circuit when same voltage is applied across the series combination of $X$ and $Y$.

An alternating voltage $V_0=100 \mathrm{V}$ with angular frequency $\omega$ is connected across the capacitor and inductor having $X_L=5 \mathrm{\Omega }$ and $X_C=10 \mathrm{\Omega }$. Find the ratio of current through inductor to $\mathrm{AC}$ source.

An uncharged capacitor $C=100 \mathrm{\mu F}$ is connected in series with a resistance $\mathrm{R} = 50 \mathrm{\Omega }$ across an $\mathrm{AC}$ source as shown in the figure. If switch $S$ is closed at $t=0$, the maximum value of $\left(V_A-V_B\right)$ is $K$ volt. Calculate $K$.

The circuit shown below consists of an $\mathrm{AC}$ source with $E_{\mathrm{rms}}=10 \mathrm{V}$. The resistances $R_1$ and $R_2$ are $3 \mathrm{\Omega }$ and $6 \mathrm{\Omega }$ respectively. If the amount of power delivered by the $\mathrm{AC}$ source in the circuit is $\alpha \mathrm{J}$. Find the value of $\alpha$.