Appendix E: Ohm's Law

Calculation of Ohm's Law in Series and Parallel Circuits

In a Series Circuit:

If we know that a potential of 120 V is applied to a circuit with 60 ohms of resistance, the amperage can be calculated by using Ohm's law. Using the values in the figure above, the equation for calculating the current flow through the series of resistors is:

If each of three resistors has a different resistance (say, 10 ohms, 20 ohms, and 30 ohms), the voltage will fluctuate between resistors. By applying a derivation of Ohm's law, V = IR, the voltage across each resistor may be calculated as:

By adding V₁ + V₂ + V₃, you can see that the sum of the potential across the individual resistors equals the total power applied to the circuit. The current (amperage) remains the same throughout a series circuit. The voltage and the resistance vary.

In a Parallel Circuit:

To calculate the total resistance for a parallel circuit, we must keep in mind that the flow in each pathway is inversely proportional to its resistance. Because voltage is constant, this value may be canceled out and the mathematical reciprocal (1/n) of the resistance may be used:

The amount of current flowing across each resistor (and path) is calculated by:

where:

Unlike series circuits, the parallel circuits have the same voltage across each path. The amperage and resistance differ from path to path. Therefore, if the voltage across one path can be calculated, the voltage for the entire circuit is known.