The charge flowing through a resistance $R$ is given by
$q = A\sin\omega t+B\cos\omega t$
The heat produced in the resistance over a very long time $\Delta t$ (much greater than $T = \dfrac{2\pi}{\omega}$ ) is:

1. $\omega^{2}\left(A^{2}+B^{2}\right) R \Delta t$

2. $\omega^{2}\left(A^{2}-B^{2}\right) R \Delta t$

3. $\dfrac{1}{2} \omega^{2}\left(A^{2}+B^{2}\right) R \Delta t$

4. $\dfrac{1}{2} \omega^{2}\left(A^{2}-B^{2}\right) R \Delta t$

Subtopic: Power factor |

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Q3:

An inductor $200$ mH, capacitor $20~\mu\text{F}$ and a resistance of $200~\Omega$ are connected in series across a source of emf, $E = (20~\text{V})\sin(500t)$ , where $t$ is in second. The power loss in the circuit is:
1. $2~\text{W}$
2. $1~\text{W}$
3. $0.5~\text{W}$
4. $0.25~\text{W}$

Subtopic: Different Types of AC Circuits |

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Q4:

In an AC-circuit, the applied voltage is

$e=V_0\sin(wt)$
and the current,

$i$ is

$i=I_0\cos(wt-\phi).$ The average power dissipated per cycle is:

1.	$V_{0} I_{0} {\cos\phi}$
2.	$\dfrac{V_{0} I_{0} \cos \phi}{2}$
3.	$V_{0} I_{0} \sin \phi$
4.	$\dfrac{V_{0} I_{0} \sin \phi}{2}$

Subtopic: Different Types of AC Circuits |

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Q1:

An AC-voltage is applied across the ends $A,B$ of the circuit shown in the figure, the RMS voltage being $V_0$ . It is observed that the RMS currents in all the three branches are equal to $\dfrac{V_0}{R}$ . The total current entering at $A$ equals:

1.	$\dfrac{V_0}{R}$	2.	$\sqrt{2}\dfrac{V_0}{R}$
3.	$\Big(\sqrt{2}+1\Big)\dfrac{V_0}{R}$	4.	$\sqrt{3}\dfrac{V_0}{R}$

Subtopic: Different Types of AC Circuits |

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Q5:

The current through the primary of a step-down transformer with a turns-ratio of

$4$ is

$1.6~\text{A}$ . The current in the secondary circuit is:
1.

$0.4~\text{A}$
2.

$0.8~\text{A}$
3.

$6.4~\text{A}$
4.

$12.8~\text{A}$

Subtopic: Transformer |

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Q6:

Sinusoidal voltages are applied at

$X$ and

$Y$ so that the currents flowing into the capacitor at

$X$ and into the resistor at

$Y$ are equal and out of phase with each other. The RMS values of the voltages across the capacitor and the resistor are each equal to

$V_r$ . The RMS value of

$V_X-V_Y$ is:

1.	zero	2.	$\sqrt 2 V_r$
3.	$2 V_r$	4.	$\dfrac{V_r}{\sqrt 2}$

Subtopic: Different Types of AC Circuits |

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Q7:

The RMS voltage across the inductor is twice that across the capacitor, while the applied RMS voltage across the entire combination (i.e.

$V_{AX}$ ) is

$V_r$ . The RMS voltage across the capacitor is:

1.	$\dfrac{V_r}{3}$	2.	$\dfrac{2V_r}{3}$
3.	$\dfrac{V_r}{2}$	4.	$V_r$

Subtopic: Different Types of AC Circuits |

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Q8:

In the given scenario, the voltage, $V_2 > V_1,$ and no current flow through the source on the left. The phase difference between the two sources is $\phi.$

Which of the following expressions correctly relates

$\phi\text{?}$

1.	$R\sin\phi= \dfrac{1}{\omega C}$	2.	$R\cos\phi= \dfrac{1}{\omega C}$
3.	$R\tan\phi= \dfrac{1}{\omega C}$	4.	$R\cot\phi= \dfrac{1}{\omega C}$

Subtopic: Different Types of AC Circuits |

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Q9:

Exactly identical voltages are imposed on the system at

$X, Y,$ and

$Z:V_m \sin \omega t$ . The peak voltage at

$O$ is

$V_o$ . Then:

1.

$V_o = V_m$
2.

$V_o < V_m$
3.

$V_o > V_m$
4. any of the above can be possible.

Subtopic: Different Types of AC Circuits |

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Q10:

A transformer has

$100$ turns in its primary. It has two secondary circuits: one with

$10$ turns and the other with

$20$ turns. The RMS voltage across the primary is

$30~\text{V}.$ The secondaries are connected to

$10~\Omega$ loads, as shown. Assuming no power loss, the RMS current in the primary is:

1.

$0.2~\text{A}$
2.

$0.15~\text{A}$
3.

$0.45~\text{A}$
4.

$0.9~\text{A}$

Subtopic: Transformer |

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1.	$\omega^{2}\left(A^{2}+B^{2}\right) R \Delta t$
2.	$\omega^{2}\left(A^{2}-B^{2}\right) R \Delta t$
3.	$\dfrac{1}{2} \omega^{2}\left(A^{2}+B^{2}\right) R \Delta t$
4.	$\dfrac{1}{2} \omega^{2}\left(A^{2}-B^{2}\right) R \Delta t$

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