# 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* = φ_{2} - φ_{1}

*V* is the voltage
between point 2 and 1 in
volts (V).

φ_{2} is the electric potential at point #2 in
volts (V).

φ_{1} 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* 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}* =

*V*

_{1 }+

*V*

_{2 }+

*V*

_{3 }+...

*V _{T}* - the equivalent voltage source or
voltage drop in volts (V).

*V*_{1} - voltage source or voltage drop in volts (V).

*V*_{2} - voltage source or voltage drop in volts
(V).

*V*_{3} - voltage source or voltage drop in volts
(V).

### Voltage in parallel

Voltage sources or voltage drops in parallel have equal voltage.

*V _{T}* =

*V*

_{1 }=

*V*

_{2 }=

*V*

_{3 }=...

*V _{T}* - the equivalent voltage source or
voltage drop in volts (V).

*V*_{1} - voltage source or voltage drop in volts
(V).

*V*_{2} - voltage source or voltage drop in volts
(V).

*V*_{3} - voltage source or voltage drop in volts
(V).

### Voltage divider

For electrical circuit with resistors (or other impedance) in
series, the voltage drop V_{i} on resistor R_{i} is:

### 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}* =
2

*V*

_{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 current ►