MODEL QUESTIONS

The emf of an AC circuit is given by$e=60 \sin \left(53.141t\right)$ and the current by $i=\frac{\left(60\right)}{10.628} \sin \left(53.141t-\frac{\mathrm{\pi }}{2}\right).$ Then the power consumed by the circuit is  _____.

The instantaneous emf of an AC circuit is given by $\epsilon =4 \sin \left(100t+\varphi \right) \mathrm{V}$. If the circuit contains an inductance of $2 \mathrm{H}$, the peak current in the circuit is ______.

An alternating current in a circuit is given by $i=i_1\sin \left(\omega t\right)+i_2\cos \left(\omega t\right)$. The RMS current in the circuit is given by _____.

An inductive coil joined to a $6 \mathrm{V}$ battery draws a steady current of  $6 \mathrm{A}.$ The coil is joined to a capacitor and an AC source of RMS voltage of $6 \mathrm{V}$ in series. If the current in the circuit is in phase with the emf, the RMS current in the circuit is _____.

Show that the average value of AC over a cycle is zero.

An AC circuit contains a variable capacitor in series with a fixed resistor. Plot any curve as capacitance is varied from zero to a very large value.

Find an expression for the average power expended in a resistor in a quarter cycle of AC.

Write the expression for the impedance of an LCR circuit and hence show the condition under which its impedance equals its resistance.