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Alternating Current

Practice Questions:

Question 1: easy

In pure inductive circuit, the curves between frequency f and reciprocal of inductive reactance 1/XL is :

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Question 2: easy

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An emf E = E0 cos (wt) applied to the circuit. The power consumed in the circuit is :

1. \[\frac{E_{0}^{2}}{R}\]

2. \[\frac{E_{0}^{2}}{2R}\]

3. \[\frac{E_{0}^{2}}{4R}\]

4. \[\frac{E_{0}^{2}}{8R}\]

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Question 3: easy

Which one of the following curves represents the variation of impedence (Z) with frequency f in series LCR circuit :-

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Question 4: easy

In series LCR circuit voltage across L, C & R is 20V each. If capacitor is short-circuited then
voltage across inductor is :

1. 20 V

2. 20√2 V

3. 10√2 V

4. 10 V

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Question 5: easy

A coil has power factor of 0.707 at 60 Hz. Then its power factor at 180 Hz will be :-

1. \[\frac{1}{\sqrt{2}}\]

2. \[\frac{1}{\sqrt{5}}\]

3. \[\frac{1}{\sqrt{10}}\]

4. \[\sqrt{\frac{5}{2}}\]

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Question 6: easy

A variable inductor is connected to an ac source. What effect does increasing the inductance have on the reactance and current in this circuit ?

1. Reactance - Decreases, Current - No change

2. Reactance - Increases, Current - Increases

3. Reactance - Decreases, Current - Increases

4. Reactance - Increases, Current - Decreases

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Question 7: easy

A variable capacitor is connected to an ac source. What effect does decreasing the capacitance have on the reactance and current in this circuit ?

1. Reactance - Decreases, Current - No change

2. Reactance - Increases, Current - Increases

3. Reactance - Decreases, Current -Increases

4. Reactance - Increases, Current -Decreases

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Question 8: easy

Given below are two statements :
Statement I : In an LCR series circuit, current is maximum at resonance.
Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit (using same resistance) when connected to same voltage source.
In the light of the above statements, choose the correct from the options given below :

1. Statement I is true but Statement II is false

2. Statement I is false but Statement II is true

3. Both Statement I and Statement II are true

4. Both Statement I and Statement II are false

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At resonance, impedance of an LCR circuit is minimum and equal to \(R\), so current is maximum. In general, impedance \(Z ge R\), hence the current \(I = V/Z\) is less than or equal to the purely resistive current \(V/R\). Thus, both statements are true.

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Question 9: easy

The maximum power is dissipated for an ac in a/an

1. Inductive circuit

2. Capacitive circuit

3. Resistive circuit

4. LC circuit

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The average power dissipated is \(P = V_{\text{rms}} I_{\text{rms}} cos \phi\). For a purely resistive circuit, the phase angle \(\phi = 0\), which gives the maximum power factor \(cos \phi = 1\).

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Question 10: easy

The peak value of the alternating current given by \(I = 4 \sin\omega t + 4 \sin(\omega t + 2\pi/3)\) is:

1. \(4\sqrt{2}\)

2. \(2\sqrt{2}\)

3. \(8\)

4. \(4\)

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The two currents can be vectorially added with phase difference \(\phi = 2\pi/3 = 120^\circ\). Resultant amplitude is \(I_0 = \sqrt{4^2 + 4^2 + 2 \times 4 \times 4 \cos 120^\circ} = 4\).

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