AC Circuits Questions

The self inductance of the motor of an electric fan is $10\text{ H}$. In order to impart maximum power at $50\text{ Hz}$, it should be connected to a capacitance of:

A circuit has a resistance of $12\Omega$ and an impedance of $15\Omega$. The power factor of the circuit will be:

The phase difference between the alternating current and emf is $\pi /2$. Which of the following cannot be the constituent of the circuit?

In a series $\text{LCR}$ circuit $R=200\Omega$ and the voltage and the frequency of the main supply is $220\text{V}$ and $50\text{Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ }$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ }$. The power dissipated in the $\text{LCR}$ circuit is:

A fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self inductance $L$ at $t=0$. The time at which the energy is stored equally between the electric and the magnetic field is: