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LR, RC and LCR Circuits

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

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

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Question 3: 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 4: 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 5: 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 6: 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 7: 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 8: easy

In LCR series circuit the values of \(L\), \(C\), \(R\) and \(E_0\) are \(0.01\text{ H}\), \(10^{-5}\text{ F}\), \(25\ \Omega\) and \(220\text{ V}\) respectively. The value of current flowing in the circuit at \(f = 0\) and \(f = \infty\) will respectively be:

1. \(8\text{ A}\) and \(0\text{ A}\)

2. \(0\text{ A}\) and \(0\text{ A}\)

3. \(8\text{ A}\) and \(8\text{ A}\)

4. \(0\text{ A}\) and \(8\text{ A}\)

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At \(f = 0\), the capacitor acts as an open circuit (\(X_C = \infty\)). At \(f = \infty\), the inductor acts as an open circuit (\(X_L = \infty\)). Therefore, current is zero in both cases.

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Question 9: easy

A bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased, while keeping the voltage of the source constant, then:

1. Bulb will give more intense light

2. Bulb will give less intense light

3. Bulb will give light of same intensity as before

4. Bulb will stop radiating light

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As frequency increases, capacitive reactance \(X_C = \frac{1}{2\pi f C}\) decreases. This decreases the total impedance \(Z = \sqrt{R^2 + X_C^2}\), thereby increasing the current, causing the bulb to glow more brightly.

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Question 10: easy

The phase difference between voltage and current in series LCR circuit at half power frequency is:

1. \(0\)

2. \(\pi/4\)

3. \(\pi/2\)

4. \(\pi\)

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At half-power frequencies, the power factor is \(\cos\phi = \frac{1}{\sqrt{2}}\), which gives \(\phi = \pi/4\).

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