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 :
An LCR series circuit with a resistance of 100 ohm is connected to an AC source of 200 V (rms) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by 60°. When only the inductor is removed the current leads the
voltage by 60°. The average power dissipated is :
In an a.c. circuit V and I are given by
V = 100 sin (100 t) volts
I = 100 sin (100t + π/3) mA
The power dissipated 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.