Alternating Current

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?

A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.

In an A.C circuit, V & I are given by V = 250 sin (100 t) volt and I = 10 sin $\left(100t+\dfrac\pi3\right)$ A respectively. The power dissipated in the circuit is:

A sinusoidal voltage V(t) = 200 sin2000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 μF and R = 100 Ω. The impedance of the circuit is _______ Ω

The value of C is ____.

The value of $\varphi$ is ____.

A resonance circuit having inductance and resistance $2\times10^{-4}$ H and 6.28 Ω respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is _______. [π = 3.14]

A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of secondary coil are 24, then the number of turns of primary are _______.

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?

The instantaneous voltages at three terminals marked $X$, $Y$ and $Z$ are given by

$$V_X = V_0\sin\omega t,\quad V_Y = V_0\sin\left(\omega t + \frac{2\pi}{3}\right)\ \text{and}\ V_Z = V_0\sin\left(\omega t + \frac{4\pi}{3}\right).$$

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$. The reading(s) of the voltmeter will be

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 :

A series LR circuit is connected to a voltage source with $V(t)=V_0\sin\Omega t$. After very large time, current I(t) behaves as $\left(t_0>>\dfrac LR\right)$ :

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to $Q_0$ and then connected to the L and R as shown below :

If a student plots graphs of the square of maximum charge ($Q^2_{\text{Max}}$) on the capacitor with time(t) for two different values $L_1$ and $L_2$ ($L_1>L_2$) of L then which of the following represents this graph correctly ? (plots are schematic and not drawn to scale)

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C', must have been connected in :

The AC voltage across a resistance can be measured using a :

At time $t=0$, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current $I(t)=I_0\cos(\omega t)$, with $I_0=1$ A and $\omega=500\ \mathrm{rad\,s^{-1}}$ starts flowing in it with the initial direction shown in the figure. At $t=\dfrac{7\pi}{6\omega}$, the key is switched from B to D. Now onwards only A and D are connected. A total charge $Q$ flows from the battery to charge the capacitor fully. If $C=20\ \mu$F, $R=10\ \Omega$ and the battery is ideal with emf of 50 V, identify the correct statement(s).

When the rms voltages $V_L$, $V_C$ and $V_R$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio $V_L:V_C:V_R=1:2:3$. If the rms voltage of the AC source is 100 V, then $V_R$ is close to :

A sinusoidal voltage $V(t)=100\sin(500t)$ is applied across a pure inductance of $L=0.02$ H. The current through the coil is :