Ohmís Law (Resistance)

The two fundamental properties of current and voltage are related by a third property known as resistance. In any electrical circuit, when voltage is applied to it, a current will result. The resistance of the conductor will determine the amount of current that flows under the given voltage. In most cases, the greater the circuit resistance, the less the current. If the resistance is reduced, then the current will increase. This relation is linear in nature and is known as Ohmís law.

By having a linearly proportional characteristic, it is meant that if one unit in the relationship increases or decreases by a certain percentage, the other variables in the relationship will increase or decrease by the same percentage. An example would be if the voltage across a resistor is doubled, then the current through the resistor doubles. It should be added that this relationship is true only if the resistance in the circuit remains constant. For it can be seen that if the resistance changes, current also changes. A graph of this relationship is shown in Figure 38, which uses a constant resistance of 20Ω. The relationship between voltage and current in this example shows voltage plotted horizontally along the X axis in values from 0 to 120 volts, and the corresponding values of current are plotted vertically in values from 0 to 6.0 amperes along the Y axis. A straight line drawn through all the points where the voltage and current lines meet represents the equation I = E⁄20 and is called a linear relationship.

Figure 38. Voltage vs. current in a constant-resistance circuit.

Ohmís law may be expressed as an equation, as follows:

Equation 1

Where I is current in amperes, E is the potential difference measured in volts, and R is the resistance measured in ohms. If any two of these circuit quantities are known, the third may be found by simple algebraic transposition. With this equation, we can calculate current in a circuit if the voltage and resistance are known. This same formula can be used to calculate voltage. By multiplying both sides of the equation 1 by R, we get an equivalent form of Ohmís law, which is:

Equation 2

E = I(R)

Finally, if we divide equation 2 by I, we will solve for resistance,

Equation 3

All three formulas presented in this section are equivalent to each other and are simply different ways of expressing Ohmís law. The various equations, which may be derived by transposing the basic law, can be easily obtained by using the triangles in Figure 39.

Figure 39. Ohmís law chart.

The triangles containing E, R, and I are divided into two parts, with E above the line and I ◊ R below it. To determine an unknown circuit quantity when the other two are known, cover the unknown quantity with a thumb. The location of the remaining uncovered letters in the triangle will indicate the mathematical operation to be performed. For example, to find I, refer to Figure 39A, and cover I with the thumb. The uncovered letters indicate that E is to be divided by R, or I = E⁄R. To find R, refer to Figure 39B, and cover R with the thumb. The result indicates that E is to be divided by I, or R = E⁄I. To find E, refer to Figure 39C, and cover E with the thumb. The result indicates I is to be multiplied by R, or E = I ◊ R.

This chart is useful when learning to use Ohmís law. It should be used to supplement the beginnerís knowledge of the algebraic method.