# Basic electrical theory

This article will outline the basic concepts of electricity: Voltage, Current, Resistance, Ohm's Law which connects them, and what Power means. (See also: Circuit Theorems)

## Ohm's law

Ohm's law

Ohm's law states that the potential difference between two points along a connected path and the current flowing through it are proportional at a given temperature:

$\mbox{V} = \mbox{I} \cdot \mbox{R}$
• V = Voltage (some countries use the symbol U)
• I = Current
• R = Resistance

## Voltage (Electric potential difference, electromotive force)

Voltage is how much energy each electron has as it moves through a wire. It is measured in Volts, which are defined as 1 Joule of energy per coulomb of electrons.

$\mbox{V} = {\mbox{J} \over \mbox{C}}$

It is the difference in two voltages that allows a current to flow. If one end of a wire is at 12 V (12 volts), and the other end at 0 V, then there is a "potential difference" of 12 V, and therefore current will flow. If there was a wire with 12 V on one end, and 5 V on the other end, then there is a potential difference of 7 V, and current will flow. In electronics, all voltages are defined relative to another voltage, usually 0 V, which may be an earth ground, or it may simply be one wire of a power supply.

• Unit: Volt
• Symbol: V
• Expressed in terms of other SI units: W/A
• Expressed in terms of SI base units: m2 · kg · s–3 · A–1

## Electric current

Electric current is the rate of charge flow past a given point in an electric circuit, measured in coulombs/second which is named ampere.

$\mbox{A} = {\mbox{C} \over \mbox{S}}$

• Unit: Ampere
• Symbol: A
• The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length.

## Electric resistance

Resistance is how much opposition a conductor gives to electrons moving through it. What is happening on a molecular level, is that electrons will hit the molecules of the conductor as they pass through, imparting a bit of their energy to the conductor, which is usually exhibited as heat.

• Unit: Ohm
• Symbol: Ω
• Expressed in terms of other SI units: V/A
• Expressed in terms of SI base units: m2 · kg · s–3 · A–2

An ohm is measured in relation to how much current will pass through the conductor for a given voltage difference. The equation relating these three quantities is Ohm's Law:

V = I * R

## Power

Power is defined as an amount of energy per time. In electronics, you will usually measure power in Watts (W), which is the voltage times the current flowing.

P = V * I

Using Ohm's law, these can be rearranged to also give

$\mbox{P} = \mbox{I}^2 * \mbox{R} = \frac{\mbox{V}^2}{\mbox{R}}$

Which are useful when the current or voltage (respectively) is a given.

• Unit: Watt
• Symbol: W
• Expressed in terms of other SI units: J/s
• Expressed in terms of SI base units: m2 · kg · s–3

## Water Analogy

It's often helpful to understand electricity in terms of water flowing in pipes. Here current is the flow of water, voltage the pressure pushing the water and resistance how easily the pipes allow the water to flow.

This diagram is an analogy to electricity's flow.

The pump is what is called the electromotive force, or EMF, and provides a pressure, measured in volts. This would be like a battery or power supply.

The water is pushed through the pipes as a current. The pipes are generally big and have only a very little resistance to this flow. These would be wires and other conductors.

Some parts of the pipe are very constricted, so they have a lot of resistance. These would be resistors (in practice these are often made of another material as well as being thin). The two "resistors" on top are in series, increasing the total resistance of the water circuit. The one on the bottom is in parallel with the other two together. It allows an alternative route for the water to flow, decreasing the total resistance.

The resistor on the bottom is more or less directly connected to the pump, so the full pressure (voltage) from the pump is across it. The two resistors on the top as a pair are also directly connected to the pump and have the full pressure (voltage), however, this pressure is divided up between them.

## Mechanical Analogy

The Mechanical analogy isn't exactly so much a way to understand electricity as a way to remember the equations, since the equations in electrical theory are often the same as those in mechanical physics theory.

 Electrical Quantity SI Unit Mechanical Quantity SI Unit Charge Coulomb Displacement Meter Current ampere Velocity Meter per second Voltage volt Force Newton Inductance Henry Mass Kilogram Elastance (reciprocal of capacitance) farad - 1 Spring constant Newton per meter Resistance Ohm Frictional drag coefficient

## Horsepower

Horsepower can also be figured by wattage. 1 HP = 746 W
In a 12 V vehicle, that equals about 64 A. There are more than one definition of horsepower and kW should be used instead in all new texts.

With real life losses for small motors and generators, it takes about 1 HP to generate 500 W, but it takes about 1 kW to produce 1HP.

## Vectors

Vectors and Phasors play an essential role in A.C. Electronics. Here are some basic examples:

$\left(3 + j4\right) - \left(6 - j8\right)= -3 + j12$

Converting this to a Vector with magnitude and phase: $\vec{M}=\sqrt{{-3}^2 +{12}^2}=3\sqrt{17}$

And phase: $\angle\gamma^\circ=tan^{-1}\frac{12}{-3}=\angle{-76}^\circ$

so we have our equivalent expressions in Polar and Rectangular Coordinate systems:

$-3 +j12 = 3\sqrt{17}\angle{-76}^\circ$

#### Multiplication

We need to be able to multiply Vectors and Phasors too.

$\left(4 +j3\right)\left(2 +j2\right)=8+j6+j6+({j^2}=-1)6=8-6+j12=2+j12$

$(5\angle{25}^\circ)(12\angle{10}^\circ)=60\angle{35}^\circ$

#### Division

It's easiest to divide once the vectors are converted from rectangular to polar.

$\frac{2+4j}{3-5j}=\frac{\sqrt{20}\angle{63.4}^\circ}{\sqrt{34}\angle{-59}^\circ}=\sqrt{\frac{20}{34}}\angle{(63.4 - -59.4)}^\circ\approx{.77}\angle{122.4}^\circ$

## Other basic electronic tips

The typical electronic device gets power from somewhere (a battery, or plugged into the wall socket), funnels it through a pile of "components" connected by wires, and has some sort of output.

Occasionally some people just let the components free float in a "rats nest", but more often people plug them into a solderless breadboard for prototyping, then later solder them into a Printed Circuit Board.