This is the explanation about “Voltage”
Voltage is commonly used as a short name for electrical potential difference. Its corresponding SI unit is the volt (not italicized). Electric potential is a hypothetically measurable physical dimension, and is denoted by the algebraic variable V (italicized )
The voltage between two (electron) positions “A” and “B”, inside a solid electrical conductor (or inside two electrically-connected, solid electrical conductors), is denoted by (VA − VB). This voltage is the electrical driving force that drives a conventional electric current in the direction A to B. Voltage can be directly measured by an “ideal voltmeter”. Well-constructed, correctly used, real voltmeters approximate very well to ideal voltmeters. For non-scientists, an analogy involving the flow of water is sometimes helpful in understanding the concept of voltage (see below).
Precise modern and historic definitions of voltage exist, but (due to the development of the electron theory of metal conduction in the period 1897 to 1933, and to developments in theoretical surface science from about 1910 to about 1950, particularly the theory of local work function) some older definitions are not now regarded as strictly correct. This is because they neglect the existence of “chemical” effects and surface effects. A particular lesson from surface science is that, to get consistency and universality, formal definitions must relate to positions or (better) electron states inside conductors.
In conduction processes occurring in metals and most other solids, electric currents consist almost exclusively of the flow of electrons in the direction B to A. This movement of electrons is controlled by differences in a so-called “total local thermodynamic potential” often denoted by the symbol µ (“mu”). This parameter is often called the “local Fermi level” or sometimes the “(local) electrochemical potential of an electron” or the “total (local) chemical potential of an electron”. The modern electron-based definition of voltage (VA − VB) is in terms of differences in µ:
,
where e is the elementary positive charge. It is sometimes convenient to put µB=0 and VB=0, and choose position “B” so that it can be a convenient reference zero for V. It is common to choose position “B” to be inside a good electrical conductor solidly connected (by a very-low-electrical-resistance path) to the local “Earth” or “Ground”. In the analysis of electrical circuit diagrams, it is common to show the point in the circuit that is being taken as the reference position B, by attaching a “Ground” (“Earth”) symbol to this point.
A common misapprehension is to assume that difference in voltage is always equal to difference in electric potential (i.e. electrostatic potential). This is often untrue, because differences in “chemical effects” (e.g., as between conductors made from different materials) also contribute to differences in µ, and hence to differences in voltage. Some textbooks (especially old physics textbooks) give historic definitions of voltage that are not strictly equivalent to the modern definition. However, the difference in value between a “voltage difference” and the related “electric potential difference” is always small (at most a few volts, often less), and in many contexts it is commonplace (and acceptable) to disregard the distinction. Nonetheless, in some contexts, such as the theory of contact potential differences, the distinction is vital.
Simple applications
Common usage (that “voltage” usually means “voltage difference”) is now resumed. Obviously, when using the term “voltage” in the shorthand sense, one must be clear about the two points between which the voltage is specified or measured. When using a voltmeter to measure voltage difference, one electrical lead of the voltmeter must be connected to the first point, one to the second point.
Voltage between two stated points
A common use 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,” can usefully be understood as the difference between two measurements. The first measurement uses one electrical lead of the voltmeter on the first terminal of the device, with the other voltmeter lead connected to ground. The second measurement is similar, but with the first voltmeter lead on the second terminal of the device. The voltage drop is the difference between the two readings. 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 voltage difference of zero. However, other pairs of points may also have a voltage difference of zero. If two such points are connected with a conductor, no current will flow through the connection.
Addition of voltages
Voltage is additive in the following sense: the voltage between A and C is the sum of the voltage between A and B and the voltage between B and C. The various voltages in a circuit can be computed using Kirchhoff’s circuit laws.
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.
Useful formulas
DC (Direct current) circuits
where V = voltage difference (SI unit: volt), I = electric current (SI unit: ampere), R = resistance (SI unit: ohm), P = power (SI unit: watt).
AC (Alternating current) circuits
Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, φ=phase difference between I and V.
AC conversions
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 Vpksin(ωt − kx), with a period T = 2π / ω, and where the angle brackets (in the root-mean-square equation) denote a time average over an entire period.
Total voltage
Voltage sources and drops in series:
Voltage sources and drops in parallel:
Where 
is the nth voltage source or drop
Voltage drops
Across a resistor (Resistor R):
Across a capacitor (Capacitor C):
Across an inductor (Inductor L):
Where V=voltage, I=current, R=resistance, X=reactance.
Measuring instruments
Instruments for measuring voltage 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 voltage 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 voltage difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the voltage difference.
