An $RC$ circuit is connected to a $10$ V AC source and it is observed to supply a $200$ mA current at a frequency of $100$ kHz. The same resistance is now paired with an inductor $(L)$ in series and the same source supplies $200$ mA current at a frequency of $1$ kHz at the same operating voltage. If the circuit were made with the given $L\text-C\text-R$ in series, the current will be a maximum when the frequency is $f_o$ . Then,

1. $f_o = \dfrac{10^3 + 10^5}{2}$ Hz

2.    $f_o > \dfrac{10^3 + 10^5}{2}$ Hz

3.    $f_o < \dfrac{10^3 + 10^5}{2}$ Hz

4.    $f_o = {10^3 + 10^5}$ Hz

Subtopic: Different Types of AC Circuits |

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Q12:

An AC source of emf

$100~\text{V}$ and frequency

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

$100~\Omega$ . A load resistance

$R_L$ 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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Q13:

In this

$LCR$ 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

$60^{\circ}.$

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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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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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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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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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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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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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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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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1.	$f_o = \dfrac{10^3 + 10^5}{2}$ Hz
2.	$f_o > \dfrac{10^3 + 10^5}{2}$ Hz
3.	$f_o < \dfrac{10^3 + 10^5}{2}$ Hz
4.	$f_o = {10^3 + 10^5}$ Hz

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