Ohm’s Law

Henry Cavendish, best known for discovering hydrogen and for measuring the density of the earth, first described the relationship between voltage, resistance, and current in an electrical circuit. Georg Simon Ohm, a German physicist, mathematician, and teacher at what we would today call a high school, proved Cavendish's theory. Earlier experimenters like André Ampère found no one-to-one relationship between electrical tension (voltage) and current. For example, if a particular wire is placed across a voltage source, a particular amount of current resulted. However, if the length of that wire was doubled, they expected the current to be cut in half. Unfortunately, their observations didn't match the expectation. The resulting current was more than half of the current with the shorter wire.Ampère decided the relationship was logarithmic.

Ohm discovered that if he applied a fixed correction to his calculations, he got linear results; doubling the length of the wire resulted in half the current. This correction corresponded to the inherent resistance of his voltage source and was applied in series with the source. This is how Ohm succeeded where others failed. Ohm also found consistent results using a thermocouple^[1] submerged in ice water^[2] instead of a voltaic pile for his voltage source. He initially used two thermocouples, one in a steam bath and one in an ice bath, but found the steam bath was unnecessary.^[3]
Ohm's testing apparatus

Ohm measured current with a torsion galvanometer. This is a magnetic needle (a compass needle) suspended over a wire such that the magnetic field surrounding the wire tries to align the needle perpendicular to the wire. The suspending wire resists the rotation of the needle such that the position of the needle corresponds to the current in the wire. For accuracy, the needle is observed with a microscope.

The modern version of Ohm's law states that if you have an electrical potential of one volt applied across a resistance of one Ohm, there will be a current flow of one ampere if the resistance is not a source of any electromotive force. Originally, Ohm's Law took the test circuit (a voltage source and a test resistance) as a whole and included a factor to account for the resistance of the voltage source. The following is the original Ohm's Law (using modern symbols where r represents the resistance of the voltage source).

I = E / (r + R)

The modern version of Ohm's law does not include a factor to account for the resistance of the voltage source. When necessary, that resistance is taken into account as a separate entity.

Mathematically, Ohm’s law can be described by the following formula:

E = I R

E = electromotive force (volts)
I = current (amperes)
R = resistance (ohms)

Ohm's law expresses the following relationship:

Consequently, resistance and current can be derived using the following formulas:

If you know any two values, you can find the other. For example, if you know your voltage and current, divide the voltage by the current to get the resistance. If you know your voltage and resistance, divide the voltage by the resistance to get the current. If you know your current and resistance, multiply them together to get the voltage.

Some people find the above diagram helpful. The E on top is a reminder that E always goes on top of the dividing line if the voltage is known (if you know the voltage, divide into it). The I and R next to each other is a reminder that if you don't know the voltage, you can find it by multiplying current and resistance (if you don't know the voltage, multiply).

It is becoming popular in some circles to express Ohm's law as V = I R, substituting V (volts) for E (electromotive force). This is improper as voltage and EMF, although manifested in the same number of volts, are not the same thing, and E is the accepted symbol for use in Ohm's Law.

Ohm's Law and power sources

By definition, Ohm's Law cannot be applied directly to power sources.^[4] For example, if you apply Ohm's Law to a battery—by dividing the battery voltage by the known internal resistance—you will get a meaningless result. This goes likewise for the secondary of a transformer (covered under transformers in AC Circuits). You cannot apply Ohm's Law directly to the secondary of a transformer because it is the source of electromotive force. To apply Ohm's Law to a power source, you must first apply any ohmic resistance in series with the voltage. This discovery by Georg Ohm made it possible for him to develop his Law in the first place.

This has caused confusion among novices and experts alike. Some, including people with advanced degrees in physics, attempt to apply Ohm's Law to wires that are the source of EMF (due to the wires being embedded in varying magnetic fields). However, mathematically applying the EMF to the low resistance of the wires produces results that don't match experimental data. They conclude that Ohm's Law (and Kirchhoff's Voltage Law, discussed later) fail under the conditions presented by the test circuit. However, mathematically applying the resistance of the said wire in series with the EMF source produces results that match the test circuit.^[5]  

Summary

The rules for Ohm's Law are:

Ohm's Law Calculations^[6]:

1. You have a resistor that is marked as 5 ohms. You place a voltmeter across the resistor and it reads 10 volts. How many amperes of current are flowing through the resistor? ____________
2. A current meter in a circuit reads 0.1 ampere. You place a voltmeter across a resistor in the circuit and the meter reads 2.5 volts. What is the resistance, in ohms, of the resistor?____________
3. A current meter in a circuit reads 2 amperes. A resistor in the circuit is labeled as 10 ohms. What voltage will be read if a voltmeter is placed across the resistor?____________
4. A 500-ohm resistor is placed across the terminals of a 12-volt battery. How much current do you expect to flow in the circuit? ____________

Ohm's Law

• Voltage is the product of current and resistance (E = IR).
• If you know any two of the following, voltage, current or resistance, you can calculate the third.
  • If you know the voltage, divide into it.
  • If you don't know the voltage, multiply.