Electrical potential difference can be thought of as the ability to move electrical charge through a resistance. At a time in physics when the word force was used loosely, the potential difference was named the electromotive force or EMF—a term which is still used in certain contexts.
Voltage is a property of an electric field, not individual electrons. An electron moving across a voltage difference experiences a net change in energy, often measured in electron-volts. This effect is analogous to a mass falling through a given height difference in a gravitational field. When using the term 'potential difference' or voltage, one must be clear about the two points between which the voltage is specified or measured. There are two ways in which the term is used. This can lead to some confusion.
Another usage of the term "voltage" is in specifying how many volts are dropped across an electrical device (such as a resistor). In this case, the "voltage," or, more accurately, the "voltage drop across the device," is really the first voltage taken, relative to ground, on one terminal of the device minus a second voltage taken, relative to ground, on the other terminal of the device. In practice, the voltage drop across a device can be measured directly and safely using a voltmeter that is isolated from ground, provided that the maximum voltage capability of the voltmeter is not exceeded.
Two points in an electric circuit that are connected by an "ideal conductor," that is, a conductor without resistance and not within a changing magnetic field, have a potential difference of zero. However, other pairs of points may also have a potential difference of zero. If two such points are connected with a conductor, no current will flow through the connection.
When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added as for direct current (DC), but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.
This hydraulic analogy is a useful method of teaching a range of electrical concepts. In a hydraulic system, the work done to move water is equal to the pressure multiplied by the volume of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to 'electrical pressure' (an old term for voltage) multiplied by the quantity of electrical charge moved. Voltage is a convenient way of quantifying the ability to do work. In relation to electric current, the larger the gradient (voltage or hydraulic) the greater the current (assuming resistance is constant).
where V = potential difference (volts), I = current intensity (amps), R = resistance (ohms), P = power (watts).
Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, φ=phasor angle between I and V
Where Vpk=peak voltage, Vppk=peak-to-peak voltage, Vavg=average voltage over a half-cycle, Vrms=effective (root mean square) voltage, and we assumed a sinusoidal wave of the form , with a period , and where the angle brackets (in the root-mean-square equation) denote a time average over an entire period.
Voltage sources and drops in series:
Voltage sources and drops in parallel:
Where is the nth voltage source or drop
Across a resistor (Resistor R):
Across a capacitor (Capacitor C):
Across an inductor (Inductor L):
Where V=voltage, I=current, R=resistance, X=reactance.
Instruments for measuring potential differences include the voltmeter, the potentiometer (measurement device), and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which, according to Ohm's Law, is proportional to the potential difference across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the potential difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the potential difference.