Assertion (A): A choke coil has the characteristic of high inductance and low resistance.
Reason (R): More is the inductive property of the choke coil, Power factor of the circuit approaches 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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A choke coil has high inductance and low resistance (A is true). Power factor is \(cos\phi = R/Z = R/sqrt{R^2 + X_L^2}\). Higher inductive property (large \(X_L\)) makes \(cos\phi\) approach minimum (0), not maximum. So R is false.
Assertion (A): Average power consumed in an \(AC\) circuit is equal to average power consumed by resistors in the circuit.
Reason (R): Average power consumed by capacitor and inductor 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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Average power in \(AC\) is \(P_{avg} = V_{rms} I_{rms} \cos\phi\). For pure inductor or capacitor, \(\phi = \pm \pi/2\) so \(cos\phi = 0\). Only resistors dissipate average power, \(P_{avg} = I_{rms}^2 R\). Hence, R correctly explains A.
Assertion (A): The power rating of an element in \(AC\) circuit refers to average power rating.
Reason (R): A given value for \(AC\) voltage or current is usually its average value.
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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Power rating of \(AC\) devices always refers to average power. However, \(AC\) voltage or current values (e.g., 220V) are typically Root Mean Square (RMS) values, not average values. For a full cycle, the average value of sinusoidal \(AC\) is zero.
Assertion (A): Average power consumed in a circuit is never negative.
Reason (R): Instantaneous power is always positive.
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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Average power consumed by passive circuits is non-negative. Instantaneous power \(p = vi\) can be negative during parts of an \(AC\) cycle, especially in reactive circuits, when energy is temporarily returned to the source.
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): Choke coil is preferred over a resistor to adjust current in an \( \text{ac} \) circuit.
Reason (R): Power factor for inductance is zero.
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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Choke coils reduce current in \( text{ac} \) circuits with minimal power loss, as power dissipation \( P = V_{rms} I_{rms} cosphi \) is low due to the phase angle approaching \( 90^circ \) for a purely inductive component. Thus, \( cosphi approx 0 \) for an ideal inductor. So, (A) and (R) are true, and (R) correctly explains (A).