Electrical Voltage

Electrical voltage is defined as electric potential difference between two points of an electric field.
Using water pipe analogy, we can visualize the voltage as height difference that makes the water flow down.

V = φ₂ - φ₁

V is the voltage between point 2 and 1 in volts (V).
φ₂ is the electric potential at point #2 in volts (V).
φ₁ is the electric potential at point #1 in volts (V).

In an electrical circuit, the electrical voltage V in volts (V) is equal to the energy consumption E in joules (J)
divided by the electric charge Q in coulombs (C).

$V=\frac{E}{Q}$

V is the voltage measured in volts (V)
E is the energy measured in joules (J)
Q is the electric charge measured in coulombs (C)

Voltage in series

The total voltage of several voltage sources or voltage drops in series is their sum.

V_T = V₁+ V₂+ V₃+...

V_T - the equivalent voltage source or voltage drop in volts (V).
V₁ - voltage source or voltage drop in volts (V).
V₂ - voltage source or voltage drop in volts (V).
V₃ - voltage source or voltage drop in volts (V).

Voltage in parallel

Voltage sources or voltage drops in parallel have equal voltage.

V_T = V₁= V₂= V₃=...

Voltage divider

For electrical circuit with resistors (or other impedance) in series, the voltage drop V_i on resistor R_i is:

$V_i=V_T\: \frac{R_i}{R_1+R_2+R_3+...}$

Kirchhoff's voltage law (KVL)

The sum of voltage drops at a current loop is zero.

∑ V_k = 0

DC circuit

Direct current (DC) is generated by a constant voltage source like a battery or DC voltage source.
The voltage drop on a resistor can be calculated from the resistor's resistance and the resistor's current, using Ohm's law:

Voltage calculation with Ohm's law

V_R = I_R × R

V_R - voltage drop on the resistor measured in volts (V)
I_R - current flow through the resistor measured in amperes (A)
R - resistance of the resistor measured in ohms (Ω)

AC circuit

Alternating current is generated by a sinusoidal voltage source.

Ohm's law

V_Z = I_Z × Z

V_Z - voltage drop on the load measured in volts (V)
I_Z - current flow through the load measured in amperes (A)
Z - impedance of the load measured in ohms (Ω)

Momentary voltage

v(t) = V_max × sin(ωt+θ)

v(t) - voltage at time t, measured in volts (V).
V_max - maximal voltage (=amplitude of sine), measured in volts (V).
ω      - angular frequency measured in radians per second (rad/s).
t        - time, measured in seconds (s).
θ       - phase of sine wave in radians (rad).

RMS (effective) voltage

V_rms = V_eff = V_max/ √2 ≈ 0.707 V_max

V_rms - RMS voltage, measured in volts (V).
V_max - maximal voltage (=amplitude of sine), measured in volts (V).

Peak-to-peak voltage

V_p-p = 2V_max

Voltage drop

Voltage drop is the drop of electrical potential or potential difference on the load in an electrical circuit.

Voltage Measurement

Electrical voltage is measured with Voltmeter. The Voltmeter is connected in parallel to the measured component or circuit.
The voltmeter has very high resistance, so it almost does not affect the measured circuit.

Voltage by Country

AC voltage supply may vary for each country.
European countries use 230V while north America countries use 120V.

Country	Voltage [Volts]	Frequency [Hertz]
Australia	230V	50Hz
Brazil	110V	60Hz
Canada	120V	60Hz
China	220V	50Hz
France	230V	50Hz
Germany	230V	50Hz
India	230V	50Hz
Ireland	230V	50Hz
Israel	230V	50Hz
Italy	230V	50Hz
Japan	100V	50/60Hz
New Zealand	230V	50Hz
Philippines	220V	60Hz
Russia	220V	50Hz
South Africa	220V	50Hz
Thailand	220V	50Hz
UK	230V	50Hz
USA	120V	60Hz

Electrical & Electronics Engineering