Ac Theory Level 3 Lesson 1 (2024)

FAQs

What is the power factor for a purely capacitive circuit is always percent? ›

The power factor is the cosine of the angle of the impedance. Since a pure capacitive circuit has no real component of the impedance, then the power factor is 0.

Looking at the graph, the current wave seems to have a “head start” on the voltage wave; the current “leads” the voltage, and the voltage “lags” behind the current. Voltage lags current by 90° in a pure capacitive circuit.

Therefore, it is true that 100% of the apparent power is used or consumed in a purely resistive circuit. This is not the case in circuits that have reactive elements, such as inductors and capacitors, where the current and voltage are out of phase with each other.

This opposition to current change is called inductive reactance (X) and is measured in ohms. Unlike resistance, the inductive ohmic value of the coil is dependent on the value of the inductor and how fast the current is changing (2лf for a sine wave).

PF = kW / kVA

A steel stamping operation runs at 100 kW (Working Power) and the Apparent Power meter records 125 kVA. To find the PF, divide 100 kW by 125 kVA to yield a PF of 80%. This means that only 80% of the incoming current does useful work and 20% is wasted through heating up the conductors.

The power factor is the ratio between Real Power and Apparent Power. It's expressed as a value between -1 and 1 and can be either inductive (lagging) or capacitive (leading). If the power factor is 1, then all of the power supplied is being used for productive work and this is called 'unity'.

Power Factor Values

For the purely resistive circuit, the power factor is 1 (perfect), because the reactive power equals zero. Here, the power triangle would look like a horizontal line, because the opposite (reactive power) side would have zero length.

Capacitance is measured in Farad (F) and is given by the formula: C = Q/V. A higher value means the capacitor is able to store more electric charges when a voltage is applied. Capacitance is a value that electronics designers pay attention to in both DC and AC circuits.

The phase relationship between current and voltage in a pure capacitive circuit is that the current leads the voltage by 90 degrees. This relationship can be understood through the mnemonic 'ELI the ICE man', where the voltage leads in an inductive circuit (ELI), but the current leads in a capacitive one (ICE).

In a purely inductive circuit, the phase relationship between the current and voltage is such that the current lags behind the voltage by 90 degrees. This means that the current waveform reaches its maximum value 1/4 of a cycle (or 90 degrees) after the voltage waveform reaches its maximum value.

What is reactive power also known by? ›

This “phantom power” is called reactive power, and it is measured in a unit called Volt-Amps-Reactive (VAR), rather than watts. The mathematical symbol for reactive power is (unfortunately) the capital letter Q.

We thus define: Apparent power: S = V x I (kVA) Active power: P = V x Ia (kW) Reactive power: Q = V x Ir (kvar)

Finally, we say that inductors in series 'block' AC because their reactance oppose changes in current. The higher the AC frequency (bigger dI in dI/dt), the higher the reactance, the more they block.

The symbol for reactance is X. To specify a specific type of reactance, a subscript is used. In this case, since it's capacitive reactance, the subscript C is used. The constant 2π comes from the number of radians in one cycle of a sinusoidal ac waveform.

The period of a wave in degrees is always 360, but the amount of time one period occupies depends on the rate voltage oscillates back and forth.

In a purely capacitive circuit, the current leads the voltage by 90° and the power factor is zero leading.

Assertion (A) : In purely capacitive AC circuit, average power consumed is zero. Reason (R) : The phase difference between the current and voltage in case of a purely capacitive circuit is 90∘.

PF expresses the ratio of true power used in a circuit to the apparent power delivered to the circuit. A 96% power factor demonstrates more efficiency than a 75% power factor. PF below 95% is considered inefficient in many regions.

For the purely resistive circuit, the power factor is 1 (perfect), because the reactive power equals zero. Here, the power triangle would look like a horizontal line, because the opposite (reactive power) side would have zero length.