# How do you calculate active power in an AC circuit?

How do you calculate active power in an AC circuit?

## 1 Answer

In an AC (Alternating Current) circuit, active power, also known as real power, is the power that is actually consumed by resistive loads and performs useful work. It is measured in watts (W) and is the component of the total power that is responsible for heating, lighting, or any other useful output.

To calculate active power in an AC circuit, you need to know the voltage (V) and current (I) at any given time. If the voltage and current are constant, you can use the formula:

Active Power (P) = Voltage (V) × Current (I) × Power Factor (PF)

However, in most AC circuits, the voltage and current vary sinusoidally over time. In such cases, you need to consider the instantaneous power at each moment and then find the average over one full AC cycle (one complete sine wave) to get the active power.

Instantaneous power (p(t)) at any given time (t) in an AC circuit is given by:

p(t) = v(t) × i(t)

Where:
v(t) = instantaneous voltage at time t
i(t) = instantaneous current at time t

Since both voltage and current are varying sinusoidally, they can be expressed as functions of time:

v(t) = Vpeak × sin(ωt)
i(t) = Ipeak × sin(ωt + φ)

Where:
Vpeak = Peak voltage amplitude
Ipeak = Peak current amplitude
ω = Angular frequency of the AC signal (2π times the frequency f)
φ = Phase angle between voltage and current waveforms

Now, to find the average active power over one full AC cycle (T), integrate the instantaneous power over one period and divide by the period:

Average Active Power (P) = (1/T) * ∫[0 to T] p(t) dt

Since the instantaneous power is proportional to the product of voltage and current, and both vary as sin(ωt), the average power over one full cycle is zero in an ideal AC circuit with perfect sinusoidal voltage and current waveforms. However, in real-world scenarios, there may be phase shifts (φ) and non-linear elements like inductive or capacitive loads that introduce a power factor (PF) less than 1, making the average power non-zero.

To avoid complex calculations, you can measure the voltage, current, and power factor using appropriate instruments, such as a multimeter and a power analyzer, to directly determine the active power consumed by an AC circuit.

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