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7. Power in an AC circuit

In case of a steady current the rate of doing work is given by,

P = Vi

In an alternating circuit, current and voltage both vary with time, so the work done by the source in time interval dt is given by

dW= Vidt

Suppose in an ac, the current is leading the voltage by an angle φ. Then we can write,

V = V0 sinωt

and = i0 sin(ωt + φ)

dW = V0i0 sin ωt sin (ωt + φ) dt

= V0 i0 (sin2 ωt cos f + sinωt cos ωt sin φ) dt

The total work done in a complete cycle is

W = V0i0 cosPower in an AC Circuit | Physics Class 12 - NEETPower in an AC Circuit | Physics Class 12 - NEET + V0i0sinPower in an AC Circuit | Physics Class 12 - NEET

Power in an AC Circuit | Physics Class 12 - NEETPower in an AC Circuit | Physics Class 12 - NEET = Power in an AC Circuit | Physics Class 12 - NEET

The average power delivered by the source is, therefore,

P = Power in an AC Circuit | Physics Class 12 - NEET = Power in an AC Circuit | Physics Class 12 - NEET = Power in an AC Circuit | Physics Class 12 - NEET

= Vrms irms cos φ

or <P>one cycle = Vrms irms cos φ

Here, the term cos φ is known as power factor.

It is said to be leading if current leads voltage, lagging if current lags voltage. Thus, a power factor of 0.5 lagging means current lags the voltage by 60° (as cos-10.5 = 60°). The product of Vrms and irms gives the apparent power. While the true power is obtained by multiplying the apparent power by the power factor cos φ. Thus,

and apparent power = Vrms × irms

True power = apparent power × power factor

For φ= 0°, the current and voltage are in phase. The power is thus, maximum (Vrms× irms). For

φ = 90°, the power is zero. The current is then stated as wattless. Such a case will arise when resistance in the circuit is zero. The circuit is purely inductive or capacitive.

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FAQs on Power in an AC Circuit - Physics Class 12 - NEET

1. What is power in an AC circuit?
Ans. Power in an AC circuit refers to the rate at which electrical energy is transferred or consumed in the circuit. It is measured in watts (W) and can be calculated using the formula: Power (P) = Voltage (V) x Current (I) x Power Factor.
2. How is power factor related to power in an AC circuit?
Ans. Power factor is a measure of how effectively electrical power is being used in an AC circuit. It determines the ratio of real power (or true power) to apparent power. The power factor affects the efficiency of the circuit and indicates the presence of reactive power. A high power factor (close to 1) indicates efficient power usage, while a low power factor signifies poor efficiency.
3. Can power flow in an AC circuit be negative?
Ans. Yes, power flow in an AC circuit can be negative. The negative power flow indicates that power is being returned from the load back to the source, which occurs in certain scenarios such as when using regenerative braking in electric vehicles or when using renewable energy sources like solar panels.
4. How does power factor correction improve the efficiency of an AC circuit?
Ans. Power factor correction is the process of adjusting the power factor of an AC circuit to make it closer to unity (1). By improving the power factor, the circuit becomes more efficient as it reduces the reactive power and minimizes losses in the transmission and distribution systems. Power factor correction also helps in reducing energy consumption and improving the overall power quality.
5. What are the different methods used for power measurement in an AC circuit?
Ans. There are several methods used for power measurement in an AC circuit, including: - Direct measurement using wattmeters or power analyzers. - Indirect measurement using current and voltage sensors along with power factor calculation. - Virtual measurement using software-based tools or simulation programs that analyze the circuit parameters. - Harmonic analysis to measure power in circuits with non-linear loads. - Integration of digital meters or smart meters that provide real-time power measurement and monitoring.
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