# Ohm's law

 Educational level: this is a secondary education resource.
 Educational level: this is a tertiary (university) resource.
V, I, and R, the parameters of Ohm's law.

## Purpose

Understand Ohm's law in the context of electronics, and the meaning of Voltage, Current, and Resistance (Resistors) in the law.

## The Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.

$I \propto V$ then:$V$ → ↑$I$ and ↓$V$ → ↓$I$

In the electrical circuit,there are three factors : current,denoted by I; potential difference, denoted by V; and resistance,denoted by R.

$I = \frac V R \;\;\;\;\;\;\; or \;\;\;\;\;\;\;V = I \cdot R$

Based on the work of Georg Simon Ohm, Ohm's law is one of three fundamental laws which begin the study of electronics, in partnership with Kirchhoff's Voltage Law and Kirchhoff's Current Law, laws. These three laws form the frame on which the rest of electronics is constructed. It's important to note that these laws don't apply everywhere, but definitely apply with great precision in wires, which are used to connect most electronic parts together in a circuit. Though individual parts may or may not be analysed by Ohm's law, their relationship to the circuit can be. Any student completing a course in electronics should be capable of quoting Ohm's law in his or her sleep. Not because they learn it once, but because it's used repeatedly in conjunction with almost every other task in electronics.

The actual statement of Ohm's Law is: The current flowing through a metallic conductor is proportional to the Electromotive force applied across its ends, provided the temperature and all other conditions remain constant.

Note there is no mention of resistance; that is simply the name given to the constant of proportionality involved.

Something important to take away from this definition is

• In a passive circuit, the current is a result of the voltage applied

and

• there are definite thermal effects on the resistance (or effective resistance) of conductors.

Ohm's law is linear and therefore assumes linearity in the electronic part. It's easy to think of the law in terms of the line equation $y = mx$ considering resistance to be the constant m, current as the independent variable x, and voltage as the dependent variable y. In this way a proportionate relationship between voltage and current is established. Of course, Ohm's law may be rearranged in three valid and easily derivable ways. It's important to be familiar with each of these and comfortable in recognising and switching between them.

$I = \frac V R \;\;\;\;\;\;\; or \;\;\;\;\;\;\;V = I \cdot R \;\;\;\;\;\;\ or \;\;\;\;\;\;\; R = \frac V I$

Example:

If you have one amp (1A) of current flowing through a 2 ohm resistor, how much voltage will be across it?
 2 volt correct, I=1, R=2, I*R=V, 1*2=2 1 volts try again, using ohm`s law 1/2 a volt Try again, did you switch current and voltage? 3 volts Try again, do not add them together, use I*R=V

### Understanding Voltage, Current, and Resistance

#### Water Flow Analogy

Electrons flow through wires like water flowing through pipes. Understanding the similarity helps one begin to appreciate voltage, current, and resistance in the context of Ohm's law. Fortunately, calculating current flow using Ohm's law is easier than water flow, because Ohm's law is linear while the laws governing water flow are not.

By imagining water flowing out of a water tower to some destination, it's clear that the weight of the water at the top of the tower pushes all of the water through the pipes to its various destinations. In this example, the water can't flow as fast through all of the pipes as others, because the pipes aren't equal. Some pipes are really skinny, others go up hills, and some are filled with unsightly gunk. Notwithstanding all of the causes of resistance in the pipes, one can imagine that the harder the water is pushed, the faster it's going to flow in the pipes.

Voltage, denoted by V (and sometimes "E", representing electromotive force), is the push of electrons through a wire, and is measured in volts. When voltage is applied to a wire it would be unwise to simply touch it, but without voltage the wire would be harmless. In the water flow analogy voltage is analogous to the weight of water in the tower pushing down through all the pipes.

Current, denoted by I, is the flow of electrons through a wire, and is measured in amperes, denoted by A. Current is caused by voltage, and is not to be confused with voltage. When doing calculations with Ohm's law the cause and effect of voltage and current is not apparent, but remembering the basic cause and effect will prevent confusion. In the water flow analogy, the current is the movement of water. Water flow rate may be expressed as some volume of water per time. Likewise the measure of current, the ampere, can be defined in terms of a quantity of electrons per time.

Resistance, denoted by R, slows or resists the electron flow in a wire, and is measured in ohms, denoted by the Greek letter for omega (Ω). Resistance is caused by anything and everything in a wire, but it is all simply measured in ohms. In the water flow analogy the resistance is caused by the restriction in the pipe itself, hills, and anything clogging the pipe.

Well, now, let us look at the formal statement: Ohm's law states that, in an electrical circuit, the current passing through a conductor is directly proportional to the potential difference applied across them under constant physical conditions.