JEE Main · 2004 · 24 Apr 2004 · Offline · Alternating Current

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for $V=5\sin (100t)$. The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $\mu$F.

For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\frac{\alpha }{10}$. The value of $\alpha$ is

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t/T)$. The r.m.s current for the period $t=0$ to $t=T$ is ______

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ______ .
( $\pi =3.14$ )

The figure given below shows an LCR series circuit with two switches ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$. When switch ${\mathrm{S}}_1$ is closed keeping ${\mathrm{S}}_2$ open, the phase difference $(\varphi )$ between the current and source voltage is $30^{\circ }$ and phase differe …

An inductor of 10 mH, capacitor of $0.1\mu \mathrm{F}$ and a resistor of $100\Omega$ are connected in series across an a.c power supply $220\mathrm{V},70\mathrm{Hz}$. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacit …