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 :
A coil has power factor of 0.707 at 60 Hz. Then its power factor at 180 Hz will be :-
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.
Average power dissipated in an AC circuit is given by \(P_{avg} = V_{rms} I_{rms} \cos \phi = I_{rms}^2 R\). Perfect inductor and capacitor have phase angle \(90^\circ\), resulting in zero power consumption.
Power consumed in A.C circuit is zero then the ac source could be connected to
The average power consumed in an AC circuit is given by \( P_{avg} = V_{rms} I_{rms} \cos \phi \). For a purely inductive or purely capacitive circuit, the phase difference \( \phi = 90^\circ \), which makes the power factor \( \cos \phi = 0 \), resulting in zero power consumption.
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.
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.
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.
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.
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.
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.
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).