In an $\text{AC}$ circuit, the power dissipated in a resistance is found to $P_1$ when a source voltage of $V_1$ is connected across it. If the same resistance is connected in series with a capacitance and the same source is connected across the combination, the power in the resistance is found to be $P_2=\dfrac{P_1}{2}.$ The phase difference between the voltage and the current is:
1. $30^{\circ}$
2. $60^{\circ}$
3. $45^{\circ}$
4. $90^{\circ}$

Subtopic: Different Types of AC Circuits |

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Q16:

An alternating current given by

I = I_{0} sin ω t + I_{0} cos ω t

$I=I_0~\sin\omega t+I_0~\cos\omega t$ flows through a circuit. The RMS current is:

1.	$I_0$	2.	$\dfrac{I_0}{\sqrt2}$
3.	$\sqrt2I_0$	4.	zero

Subtopic: RMS & Average Values |

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Q17:

The primary has

100

$100$ turns with

100

$100$ V RMS applied to it while the secondary has a total number of

20

$20$ turns, with the connection

C

$C$ made at the centre. The current

i

$i$ flowing towards

C

$C$ has the (RMS) value:

1.	$2$ A	2.	$2\sqrt2$ A
3.	$\sqrt2$ A	4.	zero

Subtopic: Transformer |

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Q18:

An alternating emf of

V = 20

$V=20$ V

s i n (100 π s^{- 1} . t)

$\mathrm{sin}(100\pi ~\text{s}^{-1}.t)$ is applied to an inductor and the peak current through the inductor is observed to be

\frac{20}{π}

$\dfrac{20}{\pi}$ A. The inductance is:

1.	$\dfrac{1}{10}$ H	2.	$\dfrac{1}{100}$ H
3.	$\dfrac{1}{1000}$ H	4.	$\dfrac{1}{10^4}$ H

Subtopic: RMS & Average Values |

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Q19:

A household ac circuit has an applied voltage of

220

$220$ V (RMS) and the current flowing through the circuit is

2.2

$2.2$ A (RMS), the phase difference between them being

60^{\circ} .

$60^\circ.$ Then:

1.	the impedance in the circuit is $100~\Omega.$
2.	the resistance in the circuit is $200~\Omega.$
3.	the power dissipated is $484$ W.
4.	all the above are true.

Subtopic: Different Types of AC Circuits |

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Q20:

An alternating emf (AC) is applied across the circuit shown in the figure. Let

V_{A X}

$V_{AX}$ be the voltage across the inductor

L,

$L,$ and

V_{X Y}

$V_{XY}$ be the voltage across the resistor

R .

$R.$ Let the angular frequency be

ω .

$\omega.$ The phase difference between

V_{X Y}

$V_{XY}$ and

V_{A X}

$V_{AX}$ :

1.	depends on the ratio $\dfrac{\omega L}{R}$
2.	depends on the quantity $\sqrt{(\omega L)^2+R^2}$
3.	depends on $L$ and $R,$ but not on $\omega$
4.	is independent of $L,R,\omega$

Subtopic: Different Types of AC Circuits |

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Q21:

Two circuits:

(1)

$(1)$ an

L - R

$L\text-R$ circuit and

(2)

$(2)$ an

R - C

$R\text-C$ circuit are driven by the same alternating current. The phase difference between the current and the voltage is twice in the

1

$1$ ^st case with respect to the

2

$2$ ^nd case and both the angles add up to

90^{\circ} .

$90^\circ.$ The resistances are equal in both cases. The ratio of their reactances (first: second) is:

1.	$\sqrt3:1$	2.	$1:\sqrt3$
3.	$3:1$	4.	$2:1$

Subtopic: Different Types of AC Circuits |

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Q14:

In which of the following cases is the RMS voltage equal to the maximum voltage in magnitude?

(A)
(B)
(C)

1. A
2. A, B
3. A, B, C
4. None of the above

Subtopic: RMS & Average Values |

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Q13:

In this

L C R

$LCR$ circuit, it is observed that the current and the voltage are in phase with each other. When the capacitor is replaced by a short circuit, the phase difference becomes

60^{\circ} .

$60^{\circ}.$

Then:

1.	$\dfrac{L}{C}=R^2$	2.	$\dfrac{L}{C}=2R^2$
3.	$\dfrac{L}{C}=3R^2$	4.	$\dfrac{L}{C}=\dfrac13R^2$

Subtopic: Different Types of AC Circuits |

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Q12:

An AC source of emf

100 V

$100~\text{V}$ and frequency

f = \frac{50}{π}

$f= \dfrac{50}{\pi}$ Hz has an internal resistance

100 Ω

$100~\Omega$ . A load resistance

R_{L}

$R_L$ is connected across the source. Maximum power is dissipated in the load, when:

1.	$R_L = 100\sqrt 2~\Omega$	2.	$R_L = \dfrac{100}{\sqrt 2}~\Omega$
3.	$R_L = 100~\Omega$	4.	$R_L = 200~\Omega$

Subtopic: Different Types of AC Circuits |

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