Voltage, or potential difference, is the difference in electric potential between two points, equal to the work needed to move one unit of charge between them. It is measured in volts, where one volt is one joule per coulomb (1 V = 1 J/C).
Learning objectives
- Define voltage and state the meaning of one volt.
- Distinguish electromotive force from terminal voltage.
- Apply Ohm’s law and Kirchhoff’s voltage law to simple circuits.
- Measure voltage correctly with a voltmeter or multimeter.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
A useful comparison is a water circuit: voltage is like the height difference or pressure that drives the flow, current is the amount of water flowing per second, and resistance is the narrowness of the pipe. If the pressure difference is zero, no water flows; if the voltage difference is zero, no current flows.
Intermediate How it behaves in a circuit
In series circuits the voltage divides between elements, and in parallel circuits each branch sees the same voltage. Kirchhoff’s voltage law formalises this: around any closed loop, the algebraic sum of voltages is zero. Voltage can be measured with a voltmeter or a multimeter in voltage mode, connected in parallel across the points of interest.
Advanced Limits, assumptions, engineering detail
Real sources have internal resistance and finite current capability, so loading matters: a high-impedance voltmeter reads close to the open-circuit EMF, while a low-impedance load pulls the terminal voltage down. Measurement leads also form loops that can pick up induced voltages in strong magnetic fields, which is one reason why twisted pairs and careful routing are used in precision measurements.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage / potential difference | V | volt (V) |
| Electromotive force | EMF | volt (V) |
| Charge | Q | coulomb (C) |
| Energy | W | joule (J) |
Worked examples
Voltage across a resistor
Problem. A 24 Ω resistor carries 0.50 A. What is the voltage across it?
Solution. V = I × R = 0.50 A × 24 Ω = 12 V.
Terminal voltage under load
Problem. A battery has an EMF of 12.6 V and an internal resistance of 0.050 Ω. What is its terminal voltage when it supplies 20 A?
Solution. Internal drop = I × r = 20 A × 0.050 Ω = 1.0 V. V_terminal = 12.6 V − 1.0 V = 11.6 V.
Practical applications
- Automotive 12 V and 24 V systems
- Mains distribution and appliance supply
- Sensor and signal circuits
- Battery and charging-system diagnostics
Automotive applications
A vehicle battery at rest typically shows an open-circuit voltage close to its nominal 12 V, and the charging system raises the voltage while the engine runs. Voltage-drop tests isolate high-resistance connections: measuring from the battery positive post to the load positive terminal while the load is on shows how much voltage is lost in the cable and connections, and the same test applies to the ground return path.
Industrial applications
Industrial distribution uses nominal voltages set by the installation standard in force, such as 230 V single-phase and 400 V three-phase in many European networks. Equipment ratings, insulation coordination, switching devices and protective devices are all selected for the system voltage and for the overvoltage category expected at that point of the installation.
Measurement procedure
- Connect the voltmeter in parallel across the two points; never connect a voltmeter in series with a load.
- Select the correct AC or DC mode and an appropriate range, starting high if the value is unknown.
- Use a meter and leads rated for the installation category and the voltage present.
- For voltage-drop tests, measure while the circuit is loaded; an unloaded measurement can hide a bad connection.
Common mistakes
- Saying that voltage flows: voltage is a difference between points, while current is what flows.
- Confusing EMF with terminal voltage: EMF is the ideal source value, terminal voltage falls as current rises.
- Connecting a voltmeter in series: the high meter resistance almost stops the current and gives a meaningless reading.
- Measuring resistance on a live circuit instead of voltage, which can damage the meter or give false readings.
Safety considerations
- Respect the meter’s voltage and CAT rating; a meter that is not suitable for the installation can arc and injure the user.
- Avoid touching the metal tips of the probes; use probes with finger guards and shrouded tips.
- Verify the meter on a known source before and after testing a hazardous circuit.