# Ohm’s Law

Part 1: Fundamental Concepts: Ohm’s Law

The one basic concept that is used most often in understanding a circuit’s operation is Ohm's law.  Ohm's law was developed by Georg Simon Ohm, a German physicist and mathematician, in 1827.  Ohm's law describes the relationship between the voltage and current in a circuit.

In our very simple flashlight circuit shown in the previous section, when the switch is closed, current flows in a loop from the battery and returns to the battery after passing through the light bulb.  This is shown again in the figure below.  The wires and switch are assumed to be perfect conductors.  We haven’t talked about the characteristics of a battery yet, so for the moment, we will treat it as an ideal voltage source — something that provides the potential to move current without any limits — it always provides the same potential.

Figure 1. Flashlight schematic with a closed switch.

If the lightbulb is removed from the circuit and the wire simply connected from the switch back around to the negative terminal of the battery (a terminal is the connection point of an electrical component), what do you imagine would happen?  There is a perfect battery providing potential and the wires are perfect conductors. With nothing to limit the amount of current in the circuit, you can imagine that there would be a very large current flowing.  Think back to the analogy used at the beginning of this chapter where water flowing though a garden hose was used.  Having a perfect battery, with a perfect conductor, is like having a faucet that can supply an unlimited amount of water flowing through a very large garden hose.  The amount of water (current) would be huge.

The lightbulb in the flashlight circuit limits the amount of current flowing through the circuit.  In the first section of this chapter, we discussed the concept that work is done (energy is released) when current flows from a more positive to a less positive potential.  That is what is happening as current flows through the light bulb.

The top of the light bulb is connected to the positive terminal of the battery though the switch.  The bottom of the light bulb is connected to the negative terminal of the battery.  Therefore, the lightbulb has a potential difference across it (one side is more positive than the other), and there is current flowing through it.  Work is being done.  In this case, that work manifests itself as light and heat coming from the light bulb.  One way of describing this is to say that the lightbulb resists the current flow, and in the process, energy is released.  It acts as sort of an energy converter, taking the potential electrical energy and converting it to light and heat when current flows.

We have discussed why conductors allow, almost perfectly, current to flow.  It is because of a physical property of the material.  The metals that are used to make conductors, primarily copper, have some of their electrons free to move with almost no bonding between them and the metal’s atoms.  These free electrons move easily under the influence of a voltage difference, allowing the current to flow nearly perfectly.

In the flashlight circuit, the metal used in the lightbulb’s filament (the part that glows) does not conduct current as freely as copper.  The tungsten filament material used is said to resist, or oppose, the flow of current.  It takes some work to detach the electrons from the filament’s tungsten atoms and move them.  In the process of doing this work, the amount of current that flows through the filament is limited.

All materials have this property.  This property is given the name electrical resistance, or more generally when used in the context of a circuit, simply resistance.  Materials with very high resistance, so much so that the amount of current that can flow through them is negligible or nonexistent, are called insulators.  Glass and most plastics, such as those used to cover wire, are examples of insulators.

There is a type of electrical component, used in most circuits, which is designed to resist current flow.  These components are called resistors.  They have one function — to dissipate power.  This seemingly useless thing to do serves a valuable function.  Resistors are normally labeled with the letter “R” in schematic diagrams.  Resistance, like voltage and current, has units.  The unit for resistance is the Ohm (abbreviated as Ω, the capital Greek letter Omega).  A resistor is aptly named.  It resists the flow of current, as opposed to a conductor (a piece of wire) that simply conducts current.

Figure 1, shown below, depicts a very simple circuit with a resistor shown in the right hand schematic.  Notice that this is the same circuit as our flashlight circuit, where the lightbulb is replaced with a resistor and a voltage source (labeled V) is used in place of the battery.  The switch, used in the flashlight schematic, has been omitted for clarity.

Figure 2. Flashlight and its equivalent circuit using a voltage source and resistor.

Looking at the figure, you can see that all of the current that leaves the voltage source moves from the positive terminal, goes through the resistor, and returns to the negative terminal.  In other words, it makes a circuit.  You can also see that the voltage present across the resistor’s terminals is the same as the voltage source because they are connected to each other with a conductor.  In this situation, we can say that the current, I, flowing through the resistor is controlled by the resistor’s resistance.  In the same way that the tungsten filament resists the current flow because it takes work to move the electrons from atom to atom, a resistor resists the current flow.  Ohm's law, the relationship between the voltage that appears across a resistor and the current that flows through it, is given by the following equation.

Equation 1.  Ohm’s Law.

In Equation 1, V is the voltage that appears across the resistor, I is the current that is flowing through it, and R is the value of the resistor in Ohms.  This simply states that the voltage that appears across a resistor is equal to the current that flows through it, multiplied by the resistance.  This very simple relationship is the foundation for understanding how circuits work.

As a side note, it is fairly common to see this relationship written as E = I * R instead of V = I * R.  This is still Ohm's law with the letter “E” standing in for “V”.  This is a matter of personal preference. Older texts, and the people that learned from them, may use E interchangeably with V.  E is shorthand for electromotive force in the same way that V is shorthand for voltage.

Let’s try adding some values to the circuit shown in Figure 1.  This is shown below in Figure 2.  In this case, there is a 5 volt power source and the goal is to find the resistance value for R that will cause 0.005 amps of current to flow through the circuit.

Plugging the values  for the voltage, V, and current, I, into Ohm's law results in:

V = I * R  so  5V = 0.005A * RΩ

Notice that the units have been left on the number for now.  Rearranging  the equation results in:

RΩ = 5V/0.005A

Solving for R yields:

R = 5/0.005  or  R = 1,000Ω

To limit the current to 0.005A in the circuit, the resistor will need to have a value of 1,000Ω.  What happens to the current if the voltage is raised to 6V?  To find out, solve Ohm's law again leaving the unknown values out:

V = I * R  so  6V = I  * 1,000Ω

Solving for I by rearranging the equation yields:

I = 6V / 1000Ω or I = 0.006A

Ohm's law can also be used to find the voltage across a resistor’s terminals if you know the current that is flowing through it.  Suppose you had a resistor of 100Ω with 0.5A flowing through it.  The voltage of the battery connected to it can be found by substituting what you know into Ohm's law:

V = I * R so V = 0.5A * 100Ω

V = 50V

Key Concepts

• The material property of resistance requires that work be done (energy is spent) to move current though the material.

• Without resistance in a circuit, an unlimited amount of current would flow in the circuit.

• Ohm’s Law (V=IR) tells you how much current flows for a given resistance with a particular voltage across it, or how much voltage appears across a resistor when there is a particular amount of current flowing through it.