AC Fundamentals

AC Current RMS (Root Mean Square)

The RMS value of an alternating current (AC) is the square root of the average of the squares of all instantaneous values over one complete cycle. It is equivalent to the DC current that delivers the same power to a load.

Formula:

• Irms = √(I₁² + I₂² + ... + In²) / n
• Where n is the number of samples or instants.

Average Value

The average value of an AC signal is the mean of all instantaneous values in one complete cycle.

Formula:

• Iavg = (1/T) ∫ I(t) dt (from 0 to T)

Peak Value

The peak value of an AC signal is the maximum instantaneous value in one complete cycle.

Form Factor

The form factor is the ratio of the RMS value to the average value of the current or voltage.

Formula:

• Form Factor = Irms / Iavg

Power

In an AC circuit, the power is the rate at which energy is delivered to a load. It can be calculated using the voltage, current, and power factor.

Formula:

• P = Vrms × Irms × cos(ϕ)

Power Factor

Power factor is the ratio of real power to apparent power in an AC circuit. It shows how effectively the current is being converted into useful work.

Formula:

• Power Factor = cos(ϕ)
• Where ϕ is the phase difference between voltage and current.

Series RL Circuit

A series RL circuit is one where a resistor (R) and inductor (L) are connected in series to an AC supply. The impedance of the circuit is a combination of resistance and inductive reactance.

Series RC Circuit

A series RC circuit consists of a resistor and a capacitor in series with the AC source. The impedance is a combination of the resistance and capacitive reactance.

Parallel RL Circuit

In a parallel RL circuit, a resistor and an inductor are connected in parallel to an AC source. The total impedance is calculated using the reciprocal of the individual impedances.

Parallel RC Circuit

A parallel RC circuit consists of a resistor and a capacitor in parallel with an AC source. The total impedance is the reciprocal of the sum of the reciprocals of the individual impedances.

Parallel RLC Circuit

A parallel RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel. The impedance of the parallel RLC circuit is the reciprocal of the sum of the reciprocals of the individual impedances.

Series Resonance

Series resonance occurs when the impedance of a series RLC circuit is minimized. This happens at a specific resonant frequency where the inductive reactance and capacitive reactance are equal in magnitude but opposite in phase.

Parallel Resonance

Parallel resonance occurs when the impedance of a parallel RLC circuit is maximized. This occurs at the resonant frequency where the total current is minimized.