# Voltage, Current, and Power

## Basic Understanding

Experiments show us that electric point charges attract or repel as calculated by Coulomb's law. Integrating (summing) over a distribution of points charges as they are assembled into a specific system configuration allows us to determine a scalar value defined as the electrical potential or electric field of a specific point. This mathematical definition is very useful in electronics circuit theory.

Voltage

The potential difference between two test points resulting from the distribution of charge in the circuit, usually measured in volts.

Current

Net amount of charge (coulombs) (number of electrons x electron charge) flowing past a specified point during a time interval (seconds), usually measured in Amps (1 Amp = 1 coulomb / 1 second). In typical components and systems the quantity of electrons is quite large and the aggregate charge flow is referred to as electricity.

Power

Energy given in a certain amount of time, usually measured in watts.

Law of Charges

Opposite charges attract while similar charges repel.

Inductance

When electricity passes through a wire it creates a moving magnetic field around the wire. The typical unit of measure is Henrys.

Capacitance

When electric fields or charge distributions are created in a physical system that stores recoverable energy, characteristics of the physical components which affect calculation of the electrical quantities are defined as capacitance. The base unit of measure is Farads, however microfarads (μF), are used much more often.

Resistance

When potential difference creates movement of electrons between two points, some of the potential energy formerly available in the system is irreversibly transferred from the electric field or the electrons moving through the component via collisions with atoms and molecules within the material. Ohm's Law, V=IR, defines resistance as R=V/I where V is the voltage difference applied across the component, I is the resulting current flow in Amps, and R is a constant created by characteristics of the component which is calculated from the measured voltage loss of the measured current passing through the component.

### Electric Field

A charged particle such as a proton or electron may "feel" an electrical force on it in a certain environment. This force is typically due to the presence of other charges nearby. The force will have a direction and magnitude, and can be represented by a vector. (A vector is simply a quantity that represents the direction and magnitude of something.) The magnitude of the force depends on the charge of the particle, the charge on the particles around it, and how close or far away they are: Highly charged particles close to each other exert heavy forces on each other; if the charges are less, or they are farther apart, the force is less. The direction of the force depends on the location of the surrounding charges.

In describing the electrical environment at that location , it is said there is an electric field at that location. The electric field is defined as the force that a single unit of charge would feel at that location. In some systems of measurement, the unit of charge is the charge of a single proton; in others it is the coulomb. A coulomb is the charge of 6.24×1018 protons

The relationship between force and electric field for a single charged particle is given by the following equation:

$\mathbf {E} =\mathbf {F} /q$ The bold letters indicate vector quantities. This means that a charge q, in an electric field E, having a certain direction and a magnitude E, would have a force F on it, in the same direction and with a magnitude F. Considering only the magnitudes, the following would result from the definition.

    E = F/q    these are all magnitudes or numerical quantities


The net electric field E, at a location is due to the presence of all other charges nearby, similar to the net electric force F, if there was a charge q at that location. The contribution of one of these other charges to the total (or net) electric field is a vector E contribution, which for a point charge can be derived from Coulomb's Law. Distributions of charge density in various shapes may also yield vector E contributions to the total electric field, to be added in as vector quantities. Practically speaking, most electricians, electrical engineers, and other electrical circuit builders and hobbyists seldom do these sorts of electric field calculations. Electric field calculations of this sort are more of a theoretical physics or special applications problem, so these calculations are omitted here in favor of more applicable material. See Electric Field for such information on electric field formulas.

There is an electrical force on a charge only if there is a charge subject to the force at a location in an electric field. However, even if there is no such charge subject to the force, there could still be an electric field at a point. This means that an electric field is a property of a location or point in space and its electrical environment, which would determine what a charge q would "feel" if it were there.

### Energy

Now, a micro-physics review: Work is causing displacement (or movement) of an object or matter against a force. Energy is the ability to perform work like this. Energy can be kinetic energy or potential energy. Kinetic energy is the energy a mass has because it is moving. Potential energy in an object, in matter, in a charge or other situation has the ability to perform work or to be converted into kinetic energy or a different kind of potential energy.

A reason why a particle or a charge may have potential energy could be because it is located at a point in a force field, such as a gravitational field, electric field, or magnetic field. In the presence of such a field, gravity or electric or magnetic forces could cause the particle or charge to move faster or move against resistive forces, representing a conversion of potential energy to kinetic energy or work. The amount of potential energy it has would depend on its location. Moving from one location to another could cause a change in its potential energy.
For example, an object near the surface of the earth placed high would have a certain amount of gravitational potential energy based on its mass, location (height or altitude) in and strength of the Earth's gravitational field. If the object were to drop from this location (height) to a new lower location, at least some of its gravitational potential energy would be converted to kinetic energy, resulting in the object moving down. The difference in gravitational potential energy could be calculated from one location to another, but determining the absolute potential energy of the object is arbitrary, so ground level is chosen arbitrarily as the height where its gravitational potential energy equals zero. The potential energy at all other heights is determined from the mass of the object, location relative to the ground level, and strength of the gravitational field.

All energy values are numerical or scalar quantities, not vectors.

### Electric Potential Energy

Somewhat similarly, a charged particle at a certain point or location in an electrical environment (i. e. an electric field) would have a certain amount of electric potential energy based on its charge, location, and the electric field there, which could be based on quantity and locations of all other charges nearby. If the charge were to move from this location to a new location or point, it could cause a change in its electric potential energy. This difference in electric potential energy in the charge particle would be proportional to its charge and it could be an increase or a decrease. From measurements and calculations, one may be able to determine this difference in electric potential energy, but coming up with an absolute figure for its potential is difficult and typically not necessary. Therefore, in a manner somewhat similar to gravitational potential energy, an arbitrary location or point nearby, often somewhere in the electric circuit in question, is chosen to be the point where the electric potential energy would be zero, if the charge were there. Often the wiring, circuit, or appliance will be connected to the ground, so this ground point is often chosen to be the zero point. The electric potential energy at all other points is determined relative to the ground level. The SI unit of electric potential energy is the joule.

### Electric Potential

Because the electric potential energy of a charged particle (or object) is proportional to its charge and otherwise simply dependent on its location (point where it's at), a useful value to use is electric potential. Electric potential (symbolized by V) at a point is defined as the electric potential energy (PE) per unit positive charge (q) that a charge would have at that given point (location). At a point a, the electric potential at a is given by:

                     Va = (PE of charge at a)/q


Somewhat analogously to an electric field, electrical potential is a property of a location and the electrical conditions there, whether or not there is a charge present there subject to these conditions. On the other hand, electric potential energy is more analogous to electric force in that for it to be present, there should be a subject charged particle or object which has that energy. Electric potential is often simply called potential by physicists. Because the SI unit of electric potential energy is the joule and because the SI unit of charge is the coulomb, the SI unit for electric potential, the volt (symbolized by V), is defined as a joule per coulomb (J/C).

Because electric potential energy is based on an arbitrary point where its value is set at as zero, the value of electric potential at a given point is also based on this same arbitrary zero point (reference point where the potential is set at zero). The potential at a given point a is then the difference between potentials from point a to the zero point, often called a ground node (or just ground).

Calculations of electric potential energy or electric potential based on Coulomb's Law are sometimes theoretically possible, such as might be for electric field calculations, but again these are of mostly theoretical interest and not often done in practical applications. Therefore, such calculations are also omitted here in favour of more applicable material.

Often it is of interest to compare the potentials at two different points, which we may call point a and point b. Then the electric potential difference between points a and b (Vab) would be defined as the electric potential at b minus the electric potential at a.

                        Vab = Vb - Va


The unit for electric potential difference is the volt, the same as for electric potential. Electric potential difference is often simply called potential difference by physicists. Under direct current (DC) conditions and at any one instant in time under alternating current (AC), potential and potential difference are numerical or scalar quantities, not vectors, and they can have positive or negative values.

### Voltage

Voltage is electric potential expressed in volts. Similarly, potential difference expressed in volts is often called voltage difference or often referred to as voltage across two points or across an electrical component. The terms electric potential, potential, and potential difference are terms more often used by physicists. Since these quantities are almost always expressed in volts (or some related unit such as millivolts), engineers, electricians, hobbyists, and common people usually use the term voltage instead of potential. Furthermore, in practical applications, electrical force, electric field, and electrical potential energy of charged particles are not discussed nearly as often as voltage, power, and energy in a macroscopic sense.

Additional note: The following explains why voltage is "analogous" to the pressure of a fluid in a pipe (although, of course, it is only an analogy, not exactly the same thing), and it also explains the strange-sounding "dimensions" of voltage. Consider the potential energy of compressed air being pumped into a tank. The energy increases with each new increment of air. Pressure is that energy divided by the volume, which we can understand intuitively. Now consider the energy of electric charge (measured in coulombs) being forced into a capacitor. Voltage is that energy per charge, so voltage is analogous to a pressure-like sort of forcefulness. Also, dimensional analysis tells us that voltage ("energy per charge") is charge per distance, the distance being between the plates of the capacitor. (More discussion is on page 16 of "Industrial Electronics," by D. J. Shanefield, Noyes Publications, Boston, 2001.)

#### Frequency

When an electric circuit is operating in Direct Current (DC) mode, all voltages and voltage differences in the circuit are typically constant (do not vary) with time. When a circuit is operating under Alternating Current (AC) conditions, the voltages in the circuit vary periodically with time; the voltages are a sinusoidal function of time, such as V(t) = a sin (b t) with constant a and b, or some similar function. The number of times the period repeats (or "cycles") per unit time is called the frequency of V(t). Under DC conditions or at any one instant in time under AC, potential (or voltage) and potential difference (or voltage difference) are numerical or scalar quantities, not vectors, and they can have positive or negative values. However, in AC mode, the overall function of voltage with time V(t), can be expressed as a complex number or a phasor for a given frequency. The frequency can be expressed in cycles per second or simply sec-1, which is called Hertz (Hz) in SI units. Typical commercial electric power provided in the United States is AC at a frequency of 60 Hz.

#### Ground

Ground is shown on electronics diagrams, but it isn't really a component. It is simply the node which has been assigned a voltage of zero. It is represented by one of the symbols below. Technically, any single node can be assigned as ground, and other voltages are measured relative to it. However, the convention is to only assign it in one of two ways, related to the type of power supply. In a single supply situation, such as a circuit powered by a single battery, the ground point is usually defined as the more negative of the power source's terminals. This makes all voltages in the circuit positive with respect to ground (usually), and is a common convention. For a split-supply device, such as a circuit driven by a center-tapped transformer, usually the center voltage is defined as ground, and there are equal and roughly symmetrical positive and negative voltages in the circuit.

Signal ground
Ground for a signal. Since wires have a certain amount of resistance to them, ground points in a circuit aren't all at exactly the same voltage. It is important in practical circuit design to separate the power supply ground from the signal ground from the shielding ground, etc. In circuits where minimum noise is especially important, power regulator circuitry should have thick wires or traces connecting the grounds, in a sequence from the power supply to the "cleanest" ground at the output of the filters of the power supply, which will then be a "star point" for the grounds of the signal circuitry.
Chassis ground
A direct connection to the chassis of the device. This is used for EMI shielding and also for safety ground in line AC powered devices.
Earth ground
Used in radio or power distribution systems, a connection to the earth itself. Also the other end of the connection for the safety ground, since the power line voltage will seek a path through the earth back to the power line supply station. This was the original usage of the word "ground", and the more modern meaning of the word would have been called a "floating ground".

The earth ground symbol and signal ground symbol are often interchanged without regard to their original meanings. As far as signal-level electronics (and this book) is concerned, ground almost always means a signal ground or floating ground, not connected to the earth itself.

### Current

Electric current, often called just current, is the movement of charge in a conductor (such as a wire) or into, out of, or through an electrical component. Current is quantified as a rate of positive charge movement past a certain point or through a cross-sectional area. Simply put, current is quantified as positive charge per unit time. However, since current is a vector quantity, the direction in which the current flows is still important. Current flow in a given direction can be positive or negative; the negative sign means that positive charges move opposite of the given direction. The quantity of current at a certain point is typically symbolized by a capital or small letter I with a designation which direction the current I is moving. The SI unit of current is the ampere (A), one of the fundamental units of physics. See ampere for the definition of ampere. Sometimes, ampere is informally abbreviated to amp. The definition of a coulomb (C), the SI unit of charge, is based on an ampere. A coulomb is the amount of positive charge passing a point when a constant one ampere current flows by the point for one second. The second is the SI unit of time. In other words, a coulomb equals an ampere-second (A·s). An ampere is a coulomb per second (C/s).

#### Conventional Current

Typically, current is in a metal and constitutes movement of electrons which have negative charge; however, people initially thought that current had a positive charge. The result is that even though current is the flow of negative electrons and flows from the negative to the positive terminal of a battery, when people do circuit analysis they pretend that current is a flow of positive particles and flows from the positive to the negative terminal of a battery (or other power source). Actually, it is more complicated than this, since current can be made up of electrons, holes, ions, protons, or any charged particle. Since the actual charge carriers are usually ignored when analyzing a circuit, current is simplified and thought of as flowing from positive to negative, and is known as conventional current.

Analogy to pebble tossing: I have pebbles and I am throwing them into a basket. In doing this the basket gains pebbles and I lose pebbles. So there is a negative current of pebbles to the basket because it is gaining pebbles, and there is a positive current of pebbles to me because I am losing pebbles. In pebble tossing the currents have equal strength but in opposite directions.

Current I is represented in amperes (A) and equals x number of y

### Power

Power is energy per unit of time. The SI unit for power is the watt (W) which equals a joule per second (J/s), with joule being the SI unit for energy and second being the SI unit for time. When somebody plugs an appliance into a receptacle to use electricity to make that appliance function, that person provides electrical energy for the appliance. The appliance usually functions by turning that electrical energy into heat, light, or work — or perhaps converts it into electrical energy again in a different form. If this situation is ongoing, it is said that the receptacle or electric power company delivers power to the appliance. The current from the receptacle going in and out of the appliance effectively carries the power and the appliance absorbs the power.

Multiplying a unit of power by a unit of time would result in a unit that represents a quantity of energy. Therefore, multiplying a kilowatt by an hour gives a kilowatt-hour (kW·h), a unit often used by electrical power companies to represent an amount of electrical energy generated or provided to consumers. Similarly, the energy capacity of batteries are often represented in units of ampere-hours (Ah) or for portable batteries, milli-Ampere-hours (mAh).

For direct current (DC), power P can be calculated by multiplying the voltage and current, when they are known.

                     P = V I


Note that energy/charge is multiplied by charge/time to give energy/time. At any one point in time t in alternating current (AC) circuitry, power P(t) equals voltage V(t) times current I(t).

         P(t) = V(t) I(t) at any one time t


Calculations of AC power averaged over time will be discussed under AC power.

## Circuit

An electronic circuit is a system in which conventional current flows from the positive terminal of a source, through a load, to the negative terminal of the source. But the current will only flow when there is a closed path from the positive to negative terminal. If there is a discontinuity or an open circuit in its path, the current will not flow and hence the circuit will be non functional. The current does not flow since the open circuit acts like an infinite resistance.

### Short Circuit

A short circuit is another name for a node, although it usually means an unintentional node. Has current through it but no voltage across it.

### Open Circuit

Has potential across it but no current through it.

### Properties of wires

Theoretical circuit connection (wire) has no resistance or inductance. Real wires always have voltage over them if there is current flowing through them (resistance). On high frequencies there are measurable voltage potentials over wire links if there is flowing alternating current through wires (inductance like in inductors).