Ohm's Law

Probably the most important mathematical relationship between voltage, current, and resistance/impedance in electricity is something called “Ohm’s Law”. A man named George Ohm published this formula in 1827 based on his experiments with electricity. This formula is used to calculate electrical values so that we can design circuits and use electricity in a useful manner. Ohm's Law is shown below.

Let’s look at what Ohm’s Law tells us. In the first version of the formula, I = V/R, Ohm's Law tells us that the electrical current in a circuit can be calculated by dividing the voltage by the resistance. In other words, the current is directly proportional to the voltage and inversely proportional to the resistance. So, an increase in the voltage will increase the current as long as the resistance is held constant. Alternately, if the resistance in a circuit is increased and the voltage does not change, the current will decrease.

The second version of the formula tells us that the voltage can be calculated if the current and the resistance in a circuit are known. It can be seen from the equation that if either the current or the resistance is increased in the circuit (while the other is unchanged), the voltage will also have to increase.

The third version of the formula tells us that we can calculate the resistance in a circuit if the voltage and current are known. If the current is held constant, an increase in voltage will result in an increase in resistance. Alternately, an increase in current while holding the voltage constant will result in a decrease in resistance. It should be noted that Ohm's law holds true for semiconductors, but for a wide variety of materials (such as metals) the resistance is fixed and does not depend on the amount of current or the amount of voltage.

As you can see, voltage, current, and resistance are mathematically, as well as, physically related to each other. We cannot deal with electricity without all three of these properties being considered.

(The symbol for an Ohm looks like a horseshoe and is pictured after the "100" in the diagram above.)

Impedance and Ohm's Law

Above, Ohm's Law was discussed for a purely resistive circuit. When there is inductive reactance or capacitive reactance also present in the circuit, Ohm's Law must be written to include the total impedance in the circuit. Therefore, Ohm's law becomes:

$I=\frac{V}{Z}$

Ohm's law now simply states that the current (I), in amperes, is proportional to the voltage (V), in volts, divided by the impedance (Z), in ohms.

Also note that when there is inductance in the circuit, the voltage and current are out of phase. This is because the voltage across the inductor will be a maximum when the rate of change of the current is greatest. For a sinusoidal wave form like AC, this is at the point where the actual current is zero. Thus the voltage applied to an inductor reaches its maximum value a quarter-cycle before the current does, and the voltage is said to lead the current by 90^o.