The power dissipated in the following circuit will be about half of its maximum value at approximately

$$\begin{gathered} 1. \omega = 1050 rad/s \\ 2. \omega =1000 rad/s \\ 3. \omega =950 rad/s \\ 4. Both \left(1\right) \& \left(3\right) \end{gathered}$$

An ac source of emf e=50 sin 100 $\pi t$ is connected across a circuit for which the phasor diagram is shown in the figure. The time difference between current and voltage applied across the circuit is

The instantaneous values of current (in ampere) and potential (in volt) in an A.C. circuit are I= 4 sin$\omega t$ and V=100cos$\left(\omega t-\begin{array}{c}\pi \\ 3\end{array}\right)$ respectively. The power factor of the circuit is

$$\begin{gathered} 1. \frac{1}{2 } \\ 2. \frac{1}{\sqrt{2}} \\ 3. 1 \\ 4. \frac{\sqrt{3}}{2} \end{gathered}$$

In the LCR series A.C. circuit, as we vary the frequency of A.C. source, peak current is obtained. The value of this peak current, apart from the supply voltage, depends upon (symbols have their usual meaning)

A direct current of 2 A and an alternating current having peak value 2 A flow through two identical resistance at the same time. The ratio of heat produced in the two resistance will be

The inductive reactance and resistance of the L-R circuit are respectively 30 ohm and 40 ohm. The impedance of the circuit is

A bulb and a capacitor are in series with an A.C. source. On increasing frequency, how will the glow of the bulb change?

In the circuit shown, X is joining to Y for a long time, and then X is joined to Z. The total heat produced in $R_2$ is ( symbols have their usual meaning)

 $$\begin{gathered} 1. \frac{L{E}^2}{2{R_1}^2} \\ 2. \frac{L{E}^2}{2{R_2}^2} \\ 3.\frac{L{E}^2}{2R_1{R}_2} \\ 4. \frac{L{E}^2{R}_2}{2{R_1}^3} \end{gathered}$$

A transformer has a turn ratio of 1: 5. A DC source of EMF 10 V is applied across its primary. EMF across the secondary will be

A series LCR circuit has resistance 2$\Omega$ and self inductance 20 mH. Bandwidth of the circuit is (in radian/s)

Voltage across the resistor, inductor and capacitor in series LCR circuit are 20 V, 50 V and 50 V respectively. Peak value of the applied source is

The r.m.s value of current for

$l= 3\sin \omega t + 4 \cos \omega t is$

In a series L-C-R circuit, different physical quantities vary with frequency $\omega$. Which of the following curves represent the correct frequency variation of the corresponding quantity?

If ${\omega }_1$ and ${\omega }_2$ are half power frequencies of a series LCR circuit, then resonant frequency ${\omega }_r$ can be expressed as

$$\begin{gathered} 1. {\omega }_r=\frac{{\omega }_1+{\omega }_2}{2} \\ 2. {\omega }_r=\sqrt{{\omega }_1{\omega }_2} \\ 3. {\omega }_r=\sqrt{\frac{{{\omega }_1}^2+{{\omega }_2}^2}{2}} \\ 4. {\omega }_r=\frac{{\omega }_1{\omega }_2}{{\omega }_1+{\omega }_2} \end{gathered}$$

Voltage and current in an ac circuit are given by V=$5\sin$$\left(100\pi t-\frac{\pi }{6}\right) V and l=4\sin \left(100\pi t+\frac{\pi }{6}\right) \mathrm{A.}$

Hence:

The r.m.s. voltage of the waveform shown is:

If potential differences measured in ac voltmeters across the inductor, capacitor, and resistor in series LCR ac circuit are 100 V, 100 V, and 50 v respectively, then the peak value of the applied ac voltage to the circuit is

1. 50 V

$$\begin{gathered} 2. 50\sqrt{2} V \\ 3. \frac{50}{\sqrt{2}} V \\ 4. \frac{100}{\pi } V \end{gathered}$$

Voltage and current in an A.C. circuit is given by $V=20\sin \left(314t\right) V and l=10\sin \left(314t+\frac{\pi }{3}\right) A.$

Wattful current in the circuit is-

$$\begin{gathered} 1. 10 A \\ 2. 5 A \\ 3. \frac{5}{\sqrt{2}}A \\ 4. \frac{10}{\sqrt{2}}A \end{gathered}$$

Which of the following devices is not based on Faraday's law of electromagnetic induction?

Current l through an inductor is increasing according to $i=2t$. Variation of the rate of increment of its energy $\left(\frac{du}{dt}\right)$ with time t is correctly shown in the graph

A time-varying current is given by $l=5\sin \left(\omega t+\begin{array}{c}\pi \\ 6\end{array}\right)$ Its r.m.s. value is (symbols have usual meanings)

$$\begin{gathered} 1. 5\sqrt{5} A \\ 2. 10 A \\ 3. \frac{5}{\sqrt{2}} A \\ 4. \frac{15}{\sqrt{2}}A \end{gathered}$$

An alternating voltage $V\sqrt{2}\sin \omega t$ at different frequencies is applied across a capacitor C as shown in the figure. Which of the following graphs between RMS current $\left(l\right)$ observed by an ammeter and angular frequency $\omega$ of voltage is correct?
             

A bulb is rated at 100 V, 100 W, and it's treated as a resistor. The inductance of an inductor (choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an ac source of 200 V and 50 Hz is

 $$\begin{gathered} 1. \frac{\pi }{\sqrt{3}}H \\ 2. 100 H \\ 3. \frac{\sqrt{2}}{\pi }H \\ 4. \frac{\sqrt{3}}{\pi }H \end{gathered}$$

The value of current in two series LCR circuit at resonance is the same when connected across a sinusoidal voltage source. Then

A: Average power in series LCR ac circuit is maximum at resonance.

R: At the resonance circuit is purely resistive.

For the circuit shown in figure below, the ammeter $A_2$ reads 1.6 A and ammeter $A_3$ read 0.4 A If ${\omega }_0$ is angular frequency and $f$ is frequency of ac, then

$$\begin{gathered} 1. {\omega }_0=\frac{4}{\sqrt{LC}} \\ 2. f=\frac{2\pi }{\sqrt{LC}} \\ 3. The ammeter A_1 reads 1.2 A \\ 4. The ammeter A_1 reads 2 A \end{gathered}$$

If the reading of $V_1$ and $V_3$ are 100 V each, the reading of $V_2$ is

If current $i_1$ = 3A sin$\omega t$ and current $i_2$ = 4A cos$\omega t$, then $i_3$ is

$$\begin{gathered} 1. 5A\sin (\omega t+53°) \\ 2. 5A\sin (\omega t+37°) \\ 3. 5A\sin (\omega t+45°) \\ 4. 5A\sin (\omega t+30°) \end{gathered}$$

A capacitor of capacitance 1 $\mu F$ is charged to a potential of 1 V. It is connected in parallel to an inductor of inductance ${10}^{-3}$H. The maximum current that will flow in the circuit has the value

$$\begin{gathered} 1. \sqrt{1000} mA \\ 2. 1 mA \\ 3. 1 \mu F \\ 4. 1000 mA \end{gathered}$$

In a box Z of unknown elements (L or R any other combination), an ac voltage $E=E_0\sin (\omega t+\varphi )$is applied and current in the circuit was found to be $I=I_0\sin (\omega t+\varphi +\frac{\pi }{4})$. Then the unknown elements in the box maybe