Voltage
claimed by DaGreeny Spring 2026
This page covers Voltage (potential difference), claimed by DaGreeny (Spring 2026)
The Main Idea
Voltage is a measure of the energy per unit charge between two points in an electric field. It describes how much work is required to move a charge between those points. Voltage can be described as the difference in Electric Potential between two points, and is what causes current to flow.
A Mathematical Model
Voltage is defined as electric potential energy per unit charge: [math]\displaystyle{ V = \frac{U}{q} }[/math], where
[math]\displaystyle{ V }[/math] = voltage (volts)
[math]\displaystyle{ U }[/math] = electric potential energy (joules)
[math]\displaystyle{ q }[/math] = charge (coulombs)
Work done by an electric field:
[math]\displaystyle{ W = qV }[/math]
Voltage in terms of the electric field:
[math]\displaystyle{ V = - \int \vec{E} \cdot d\vec{\ell} }[/math]
Ohm’s Law (circuit relationship):
[math]\displaystyle{ V = IR }[/math]
Where:
[math]\displaystyle{ I }[/math] = current
[math]\displaystyle{ R }[/math] = resistance
A Computational Model
Link to PHET imulation [[1]]
Examples
Examples
Easy
Problem: A charge of [math]\displaystyle{ q = 2 \ \text{C} }[/math] moves between two points and loses [math]\displaystyle{ U = 10 \ \text{J} }[/math] of electric potential energy. What is the voltage difference between the two points? Solution: Start with the definition of voltage: [math]\displaystyle{ V = \frac{U}{q} }[/math] Substitute values: [math]\displaystyle{ V = \frac{10}{2} }[/math] [math]\displaystyle{ V = 5 \ \text{V} }[/math] Answer: [math]\displaystyle{ 5 \ \text{V} }[/math]
Medium
Problem: A resistor with resistance [math]\displaystyle{ R = 6 \ \Omega }[/math] has a current of [math]\displaystyle{ I = 3 \ \text{A} }[/math] flowing through it.
What is the voltage across the resistor?
How much energy is transferred to the resistor in [math]\displaystyle{ t = 4 \ \text{s} }[/math]?
Solution: Step 1: Find voltage using Ohm’s Law [math]\displaystyle{ V = IR }[/math] [math]\displaystyle{ V = (3)(6) }[/math] [math]\displaystyle{ V = 18 \ \text{V} }[/math]
Step 2: Find energy transferred Use: [math]\displaystyle{ W = VIt }[/math] Substitute values: [math]\displaystyle{ W = (18)(3)(4) }[/math] [math]\displaystyle{ W = 216 \ \text{J} }[/math]
Answer: Voltage: [math]\displaystyle{ 18 \ \text{V} }[/math] Energy transferred: [math]\displaystyle{ 216 \ \text{J} }[/math]
Connectedness
Voltage is essential in everyday electronics like phones, laptops, and gaming systems, where different components require precise voltage levels. In engineering (especially electrical/computer), voltage is central to circuit design, signal processing, and power systems. Industrial applications include power transmission (high voltage reduces energy loss), semiconductor design, electric vehicles, and telecommunications systems.
History
Allesandro Volta invented the first battery in Italy around 1800, creating the first continuous source of electric potential. Because of this, the unit "Volt", and thus Voltage, is named after him.
See also
Further reading
Introduction to Electrodynamics by David J. Griffiths
The Feynman Lectures on Physics, Volume II by Richard Feynman
Electric Circuits by Nilsson and Riedel
References
OpenStax University Physics Volume 2
MIT OpenCourseWare: Electricity and Magnetism
Khan Academy: Electric Potential and Voltage