A capacitor and a resistor of resistance $100 \sqrt{3} \Omega$ are connected in series to an AC source of voltage $100 \sin (200 t) \mathrm{V}$, where ' $t$ ' is time in second. If the phase difference between the voltage and the current in the circuit is $30^{\circ}$, then the capacitance of the capacitor is

An electric bulb, an open coil inductor, an AC source and a key are all connected in series to form a closed circuit. They key is closed and after some time an iron rod is inserted into the interior of the inductor, then

An inductor and a resistor are connected in series to an AC supply. If the potential difference across the inductor and the resistor are 180 V and 240 V respectively, then the voltage of the AC supply is

The frequency of an alternating voltage is 50 Hz . The time taken for instantaneous voltage to increase from zero to half of its peak voltage is

A coil has a resistance of $30 \Omega$ and an inductive reactance of $20 \Omega$ at 50 Hz frequency. If an AC source of $200 \mathrm{~V}, 100 \mathrm{~Hz}$ is connected across the coil, the current in the coil is

At very high frequencies, the current ( $i$ ) in the given circuit is

An alternating emf given by the equation $E=200 \sin (50 \pi t)$ (where, $E$ is in volts and $t$ is in seconds) is applied across a series combination of an inductor and a resistor having inductive reactance $40 \Omega$ and resistance $30 \Omega$ respectively. At time $t=1 \mathrm{~s}$, the power dissipated by the resistor is close to $\left(\cos 53^{\circ}=0.6\right)$

A series $L-C-R$ circuit is connected to an AC source of voltage $150 \sin (80 \pi t)$ volt. 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 an ideal step up transformer, if the input voltage and input power are $V_1$ and $R_1$ respectively and the output voltage and output power are $V_2$ and $P_2$ respectively, then

A generator produces a current of 100 A at 4000 V . The voltage is stepped up to $2 \times 10^5 \mathrm{~V}$ by a transformer before being sent on a high voltage transmission line of resistance $50 \Omega$. The percentage of power loss in the transmission line is

A capacitor of capacitance $100 \mu \mathrm{~F}$ and a coil of resistance $20 \Omega$ and inductance 12.5 mH are connected in series with a $220 \mathrm{~V}, \frac{200}{\pi} \mathrm{~Hz}, \mathrm{AC}$ source. The maximum value of instantaneous current in the circuit is

The $Q$ value of a series $L-C-R$ circuit with $L=2 \mathrm{H}$, $C=32 \mu \mathrm{~F}, R=20 \Omega$ is

A resistor of resistance of $100 \Omega$ is connected to an AC source $\varepsilon=10 \sin (250 \pi) t$. The energy dissipated as heat during $t=0$ to $t=1 \mathrm{~ms}$ is approximately.

A $2 \mu \mathrm{~F}$ capacitor is charged to 50 V by a battery. The battery is removed after capacitor if fully charged. At time $t=0$, a 10 mH coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is

An AC current is given by the expression, $I(t)=50 \sin (200 \pi t)$ in amperes. The frequency and rms value of the current, respectively are

For an $R$ - $L-C$ circuit, driven with voltage of amplitude $V_m$ and frequency $\omega_0=\frac{1}{\sqrt{L C}}$, the current exhibits resonance. The quality factor $Q$ is

Which one of the following curves represents the variation of impedance ( $Z$ ) with frequency $f$ in a series $L-C-R$ circuit, when connected to an AC source?

An alternating voltage $\varepsilon=30 \sin 200 t$ (in volts) is applied to the circuit below. The amplitude of the current through the circuit is