Reactance and impedance

The figure given below shows an $LCR$ series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference ($\phi$) between the current and source voltage is 30° and phase difference is 60° when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1-L_2)$ is ________ H.

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

A circuit with an electrical load having impedance $Z$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $V(t) = 300\sin(400t)$ V, where $t$ is time in s. List-I shows various options for the load. The possible currents $i(t)$ in the circuit as a function of time are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is $\dfrac{\sqrt a}\pi$ A. The value of $a$ is ______.

A sinusoidal voltage $V(t)=210\sin3000t$ volt is applied to a series LCR circuit in which $L=10$ mH, $C=25\ \mu$F and $R=100\ \Omega$. The phase difference ($\Phi$) between the applied voltage and resultant current will be :

In a series LCR circuit, the inductance, capacitance and resistance are $L=100$ mH, $C=100\ \mu$F and $R=10\ \Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ______ A.

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$F and a resistance of 120 $\Omega$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/°C will get heated by 16°C is ______ s.

In the given circuit, the magnitude of $V_L$ and $V_C$ are twice that of $V_R$. Given that $f=50$ Hz, the inductance of the coil is $\dfrac1{K\pi}$ mH. The value of K is ______.

The rms value of conduction current in a parallel plate capacitor is 6.9 $\mu$A. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be :

The effective current I in the given circuit at very high frequencies will be ______ A.

To light, a 50 W, 100 V lamp is connected, in series with a capacitor of capacitance $\dfrac{50}{\pi\sqrt x}$ μF, with 200 V, 50 Hz AC source. The value of $x$ will be ______.

A series LCR circuit has L = 0.01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude $(V_m)$ 50 V. At frequency 60% lower than resonant frequency, the amplitude of current will be approximately :

The equation of current in a purely inductive circuit is $5\sin(49\pi t-30^\circ)$. If the inductance is 30 mH then the equation for the voltage across the inductor, will be :

$\left\{\text{Let }\pi=\dfrac{22}7\right\}$

An alternating emf $E=440\sin100\pi t$ is applied to a circuit containing an inductance of $\dfrac{\sqrt2}\pi$ H. If an a.c. ammeter is connected in the circuit, its reading will be :

A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\dfrac\pi2$. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?

The value of C is ____.

The value of $\varphi$ is ____.

In the circuit shown, $L = 1\ \mu$H, $C = 1\ \mu$F and $R = 1$ kΩ. They are connected in series with an a.c. source $V = V_0\sin\omega t$ as shown. Which of the following options is/are correct?

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R = 5 Ω, L = 25 mH and C = 1000 μF. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :