ELC-25

AC power P=VI cosφ

P = V I cosφ, Q = V I sinφ, S = V I. Single-phase rms.

Reading speed

PowerAC single phase

Governing equation

P=VI\cos\varphi,\quad Q=VI\sin\varphi

where

V: Voltage rms (V)
I: Current rms (A)
\varphi: Phase angle (°)
P: Active power (W)
Q: Reactive power (var)

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-25 — AC power P=VI cosφ) is the form associated with AC single phase. Working symbols: $V$ , $I$ , $\varphi$ $\rightarrow$ $P$ , $Q$ . The average of instantaneous p = v i over a period is Vrms Irms cosφ, the angle between the phasors.

Purpose

Purpose: compute

P

Q

from

V

I

\varphi

in Electrical via

P=VI\cos\varphi,\quad Q=VI\sin\varphi

P = V I cosφ, Q = V I sinφ, S = V I. Single-phase rms. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 230.000\,\mathrm{V}

I = 10.000\,\mathrm{A}

\varphi = 30.000\,\mathrm{^{\circ}}

, the governing relation

P=VI\cos\varphi,\quad Q=VI\sin\varphi

yields

P = 1991.9\,\mathrm{W}

Q = 1150.0\,\mathrm{var}

. A source, a lagging current, a P–Q pair. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Voltage rms V230 VCurrent rms I10 APhase angle \varphi30 °

Outputs

Active power P1991.9 W
Reactive power Q1150.0 var

Reading speed

Watch on YouTube

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Narration of this film

A source, a lagging current, a P–Q pair.

The average of instantaneous p = v i over a period is Vrms Irms cosφ, the angle between the phasors.

Reading speed

Watch on YouTube