Core quantities
Electric charge is conserved and comes in whole multiples of the elementary charge e. Current is the rate at which charge flows, voltage is the energy per unit charge between two points, and resistance is how strongly a component opposes current for a given voltage.
| Term | Symbol | SI unit | Definition or formula |
|---|---|---|---|
| Electric charge | Q or q | coulomb (C) | Q = n·e, with e = 1.602176634 × 10⁻¹⁹ C |
| Electric current | I | ampere (A) | I = ΔQ/Δt (charge per unit time) |
| Voltage (potential difference) | V or U | volt (V) | V = W/Q (work per unit charge) |
| Electromotive force | ε | volt (V) | energy per unit charge supplied by a source such as a battery |
| Resistance | R | ohm (Ω) | R = V/I; for a uniform conductor R = ρL/A |
| Resistivity | ρ | ohm metre (Ω·m) | material property; R = ρL/A |
| Conductance | G | siemens (S) | G = 1/R = I/V |
| Electric power | P | watt (W) | P = V·I = I²R = V²/R |
| Electrical energy | E or W | joule (J), kWh | E = P·t |
| Electric field | E | volt per metre (V/m) = N/C | E = F/q (force per unit test charge) |
| Capacitance | C | farad (F) | C = Q/V |
| Inductance | L | henry (H) | V = L·dI/dt |
Sources: OpenStax: University Physics Volume 2, 5.1 Electric Charge; OpenStax: University Physics Volume 2, 9.1 Electrical Current; OpenStax: University Physics Volume 2, 7.1 Electric Potential Energy; OpenStax: University Physics Volume 2, 10.1 Electromotive Force; OpenStax: University Physics Volume 2, 9.3 Resistivity and Resistance; OpenStax: University Physics Volume 2, 9.5 Electrical Energy and Power; OpenStax: University Physics Volume 2, 5.4 Electric Field
Efficiency and power factor
Efficiency is the fraction of input power that a device delivers as useful output: η = P_out / P_in, usually written as a percentage. The rest is lost, mostly as heat, so η is always below 100% for real equipment.
In AC circuits, real power P (W), reactive power Q (var) and apparent power S (VA) form a right triangle: S² = P² + Q². Power factor is PF = P / S. For sinusoidal voltage and current, PF = cos φ, where φ is the phase angle between them; PF = 1 for a purely resistive load.
| Quantity | Symbol | Unit | Formula |
|---|---|---|---|
| Apparent power | S | VA | S = V_rms × I_rms |
| Real (active) power | P | W | P = V_rms × I_rms × cos φ |
| Reactive power | Q | var | Q = V_rms × I_rms × sin φ |
| Power factor | PF | none | PF = P / S = cos φ |
| Three-phase real power | P | W | P = √3 × V_LL × I_L × PF |
| Efficiency | η | % | η = P_out / P_in × 100% |
Sources: OpenStax: University Physics Volume 2, 15.4 Power in an AC Circuit
AC and DC circuits
In a direct-current (DC) circuit the current flows in one direction and the voltage has a constant polarity, as from a battery or a solar cell. Ohm's law and P = VI apply directly to the steady values.
In an alternating-current (AC) circuit the voltage and current reverse direction periodically, usually as a sine wave at 50 Hz or 60 Hz for mains power. Calculations use RMS values; for a sine wave V_rms = V_peak / √2. Capacitors and inductors add reactance, which shifts current out of phase with voltage and makes the power factor less than 1.
Sources: OpenStax: University Physics Volume 2, 15.1 AC Sources; OpenStax: University Physics Volume 2, 15.4 Power in an AC Circuit