Assertion (A): At resonance in AC circuits current and emf are in phase.
Reason (R): At resonance in AC circuits, current is maximum.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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At resonance, the inductive reactance \(X_L\) equals the capacitive reactance \(X_C\), making the total impedance purely resistive \(Z=R\). This results in the current and emf being in phase. Since impedance is minimal \(Z=R\), the current is maximal. Therefore, R is the correct explanation of A.
Assertion (A): At frequency greater than resonant frequency, circuit is inductive in nature.
Reason (R): Reciprocal of reactance is called susceptance.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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For frequencies greater than resonant frequency, inductive reactance \(X_L = \omega L\) becomes greater than capacitive reactance \(X_C = 1/(\omega C)\), making the circuit inductive. The reciprocal of reactance is defined as susceptance. Both statements are true, but R does not explain A.
Assertion (A): If the resistance of a series resonant LCR circuit is decreased, then the peak current versus frequency graph will be taller and narrower.
Reason (R): If the resistance of a series resonant LCR circuit decreased, then its resonance will be unaffected.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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When resistance \(R\) in a series \(LCR\) circuit decreases, the peak current \(I_{max} = V/R\) at resonance increases, making the peak taller. The quality factor \(Q = (\omega_0 L)/R\) increases, leading to a narrower resonance curve. The resonant frequency \(omega_0 = 1/\sqrt{LC}\) remains unchanged, but the overall resonance behavior (sharpness, peak current) is affected. Therefore, (A) is true and (R) is false.
Assertion (A): The impedance of series L-C-R circuit can be greater, equal or less than the resistance.
Reason (R): The minimum impedance of series LCR circuit depends over angular frequency of applied emf.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The impedance of a series \(LCR\) circuit is given by \(Z = \sqrt{R^2 + (X_L - X_C)^2}\). Since \((X_L - X_C)^2\) is always non-negative, \(Z\) is always greater than or equal to \(R\). Thus, (A) is false. The minimum impedance occurs at resonance, where \(Z_{min} = R\). This minimum value depends only on \(R\) and not on the angular frequency \(omega\). Thus, (R) is also false.
Assertion (A): A capacitor of suitable capacitance can be used in an A.C. circuit in place of the choke coil.
Reason (R): A capacitor blocks D.C. and allows A.C. only.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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A choke coil is an inductor with high inductance and low resistance, used to limit AC current without much power loss. A capacitor also provides reactance \(X_C = 1/(\omega C)\) in an AC circuit, limiting AC current without dissipating significant power. Thus, a capacitor of suitable capacitance can indeed replace a choke coil for AC current limiting applications, so (A) is true. Reason (R) states that a capacitor blocks DC and allows AC, which is a fundamental property of a capacitor. This property (allowing AC) is why it can function as a reactive element in AC circuits, including current limiting, similar to a choke coil. Therefore, (R) is the correct explanation for (A).
Assertion (A): When frequency is greater than resonance frequency in a series LCR circuit, it will be an inductive circuit.
Reason (R): Resultant Voltage Will lead the current.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
When frequency \(f > f_r\) in a series LCR circuit, the inductive reactance \(X_L\) is greater than the capacitive reactance \(X_C\). This makes the circuit inductive. In an inductive circuit, the resultant voltage leads the current. Hence, both assertion and reason are true, and the reason correctly explains the assertion.
Assertion (A): The moving coil ammeters or voltmeters can’t be employed to measure alternating current or voltage respectively.
Reason (R): If an alternating current is passed through a moving coil ammeter or voltmeter, then the average value of torque experienced by the coil is zero.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Moving coil instruments measure the average value of current. For AC, the average value over a full cycle is zero, resulting in zero average torque. Hence, moving coil ammeters/voltmeters cannot measure AC. Both assertion and reason are true, and the reason correctly explains the assertion.
Assertion (A): In ac supply we cannot feel any fluctuations of current in bulbs.
Reason (R): House hold ac supply has very low frequency.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Our eyes cannot detect flickers above \(10-15 \text{ Hz}\). Household AC supply (\(50/60 \text{ Hz}\)) changes too rapidly for us to perceive fluctuations in bulbs. Thus, Assertion (A) is true. However, \(50/60 \text{ Hz}\) is not considered a "very low frequency", thus Reason (R) is false.
Assertion (A): \(220V\), \(50 \text{ Hz}\) appliance implies that potential difference in bulb is always \(220V\).
Reason (R): Every appliance is specified with its peak tolerable voltage.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
\(220V\) AC represents the RMS voltage, not the instantaneous or peak voltage. The instantaneous voltage varies sinusoidally, reaching a peak of \(V_{\text{peak}} = V_{\text{RMS}} \sqrt{2} = 220 \sqrt{2} \approx 311 \text{V}\). So, Assertion (A) is false. Appliances are usually specified by their RMS operating voltage, not peak tolerable voltage. So, Reason (R) is false. Both assertion and reason are false.
Assertion (A): Transformer does not work on \( \text{dc} \).
Reason (R): \( \text{dc} \) neither changes in magnitude nor in direction.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Transformers operate on the principle of mutual induction, requiring a changing magnetic flux. \( text{dc} \) current produces a constant magnetic field, thus no change in flux and no induced EMF. Hence, (A) is true. \( text{dc} \) current indeed has constant magnitude and direction, so (R) is also true and correctly explains (A).