An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts as shown in fig. The potential difference across L, C and R is 40 V, 10 V and 40V, respectively. The amplitude of the current flowing through the LCR series circuit is \(10\sqrt{2}~A\). The impedance of the circuit will be:

1. $4\Omega $

2. $5\Omega $

3. $4\sqrt{2}\Omega $

4. $5/\sqrt{2}\Omega $

Subtopic: Different Types of AC Circuits |

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A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

1. 2 A

2. 4 A

3. 0.2 A

4. 0.4 A

Subtopic: Transformer |

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A series LCR circuit containing 5.0 H inductor, \(80~\mu F\) capacitor and 40 $\mathrm{\Omega}$ resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

1. 46 rad/s and 54 rad/s

2. 42 rad/s and 58 rad/s

3. 25 rad/s and 75 rad/s

4. 50 rad/s and 25 rad/s

Subtopic: Different Types of AC Circuits |

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A 40 $\mathrm{\mu}$F capacitor is connected to a 200 V, 50 Hz ac supply. The RMS value of the current in the circuit is, nearly:

1. 2.05 A

2. 2.5 A

3. 25.1 A

4. 1.7 A

Subtopic: RMS & Average Values |

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An ac voltage source is connected to a series LCR circuit. When L is removed from the circuit, the phase difference between current and voltage is π/3. If C is instead removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is:

1. 0.5

2. 1.0

3. $-1.0$

4. Zero

Subtopic: Power factor |

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A light bulb and an inductor coil are connected to an ac source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb:

1. decreases

2. remains unchanged

3. will fluctuate

4. increases

Subtopic: Different Types of AC Circuits |

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The variation of EMF with time for four types of generators is shown in the figures. Which amongst them can be called AC?

1. (a) and (d)

2. (a), (b), (c), (d)

3. (a) and (b)

4. only (a)

Subtopic: AC Generator |

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A circuit when connected to an AC source of 12 V gives a current of 0.2 A. The same circuit when connected to a DC source of 12 V, gives a current of 0.4 A. The circuit is:

1. series LR

2. series RC

3. series LC

4. series LCR

Subtopic: Different Types of AC Circuits |

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The peak voltage of the ac source is equal to:

1.\(1 / \sqrt{2}\) times the rms value of the ac source

2. the value of voltage supplied to the circuit

3. the rms value of the ac source

4. \(\sqrt{2}\) times the rms value of the ac source

1.\(1 / \sqrt{2}\) times the rms value of the ac source

2. the value of voltage supplied to the circuit

3. the rms value of the ac source

4. \(\sqrt{2}\) times the rms value of the ac source

Subtopic: RMS & Average Values |

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A series LCR circuit with inductance 10 H, capacitance 10 \(\mu F\), resistance 50 \(\Omega\) is connected to an ac source of voltage, V = 200 sin(100 t) volt. If the resonant frequency of the LCR circuit is \(\nu_0\) and the frequency of the ac source is \(\nu\), then:

1. \(\nu=100 \mathrm{~Hz} ; ~\nu_0=\frac{100}{\pi} \mathrm{~Hz}\)

2. \(\nu_0=\nu=50 \mathrm{~Hz}\)

3. \(\nu_0=\nu=\frac{50}{\pi} \mathrm{Hz}\)

4. \(\nu_{0}=\frac{50}{\pi} \mathrm{Hz}, \nu=50 \mathrm{~Hz}\)

1. \(\nu=100 \mathrm{~Hz} ; ~\nu_0=\frac{100}{\pi} \mathrm{~Hz}\)

2. \(\nu_0=\nu=50 \mathrm{~Hz}\)

3. \(\nu_0=\nu=\frac{50}{\pi} \mathrm{Hz}\)

4. \(\nu_{0}=\frac{50}{\pi} \mathrm{Hz}, \nu=50 \mathrm{~Hz}\)

Subtopic: Different Types of AC Circuits |

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