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 Ω

2.  5 Ω

3. 42 Ω

4. 5/2 Ω

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 Ω 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 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 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
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.  \(\nu_{0}=\frac{50}{\pi} \mathrm{Hz}, \nu=50 \mathrm{~Hz}\)
Subtopic:  Different Types of AC Circuits |
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An a.c. source given by V = Vsin\(\omega t\) is connected to a pure inductor L in a circuit and Im is the peak value of the ac current. The instantaneous power supplied to the inductor is:
1.  \(\frac{V_mI_m}{2}sin(2\omega t)\)
2.  \(-\frac{V_mI_m}{2}sin(2\omega t)\)
3.  \({V_mI_m}sin^{2}(\omega t)\)
4.  \(-{V_mI_m}sin^{2}(\omega t)\)

Subtopic:  Different Types of AC Circuits |
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Given below are two statements:
Statement-I: In an ac circuit, the current through a capacitor leads the voltage across it.
Statement-II: In ac circuits containing pure capacitance only, the phase difference between the current and the voltage is \(\pi\)
In light of the above statements, choose the most appropriate answer from the options given below:
1.  Both statement-I and statement-II are correct
2.  Both statement-I and statement-II are incorrect
3.  Statement-I is correct but statement-II is incorrect
4.  Statement-I is incorrect but statement-II is correct
Subtopic:  Different Types of AC Circuits |
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An inductor of inductance 2 mH is connected to a 220 V, 50 Hz ac source. Let the inductive reactance in the circuit is X1. If a 220 V dc source replaces the ac source in the circuit, then the inductive reactance in the circuit is X2. X1 and X2 , respectively, are:
1.  6.28 \(\Omega\), zero
2.  6.28 \(\Omega\), infinity
3.  0.628 \(\Omega\), zero
4.  0.628 \(\Omega\), infinity
Subtopic:  Different Types of AC Circuits |
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A standard filament lamp consumes 100 W when connected to 200 V ac mains supply. The peak current through the bulb will be:
1.  0.707 A
2.  1 A
3.  1.414 A
4.  2 A
Subtopic:  RMS & Average Values |
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