Parallel Circuits

In Parallel Circuits, the loads are connected across the power line to form branches. The loads operate independently of each other, and therefore a break in any one branch does not prevent the line voltage from being applied to the remaining branches. The result is that one path (branch) can be open with the load not receiving current without the other loads being affected, as in the newer strings of holiday lights.

Current has a number of paths to follow. If all paths are available, the current divides itself between the branches back to the source. If a path is open, the current divides between the remaining available paths and goes back to the source. Parallel circuits are used in the majority of industrial, commercial and residential applications of electricity.

The next two circuit illustrations show three resistors in parallel. The only difference between the two circuits is the resistor values. To use Ohm's Law to solve the equations, you need to know how resistance, current and voltage behave in parallel circuits. The total resistance (RT) of a parallel circuit decreases as more branches are added. The total resistance of a parallel circuit is always less than the resistance of any of its branches and is therefore less than the value of the lowest resistance in the circuit.

To determine total resistance (RT) two different formulas are used:

• Resistors with equal values
• Resistors with unequal values

Resistors with Equal Values: This RT is determined by dividing the value of one of the resistors by the total number of resistors in the circuit. Using this formula, the total resistance for the first circuit is calculated to be four ohms.

Resistors with Unequal Values: Calculating RT is more complicated and is shown below:

As a point of interest, the RT for this circuit is 1.09W.

To determine current, you need to find the total current, which is the sum of all currents in all the branches. The following simple formula represents the total current (IT), and the illustration offers a demonstration.

To determine the individual branch currents, it is necessary to know whether or not all the resistors have the same value.

Current with Equal Resistor Values: The current divides equally. Divide the total current by the total number of branch resistors to determine the current flowing through each branch. The following illustration and calculation demonstrate this procedure.

Current with Unequal Resistor Values: The current is greater through the branch with the least resistance.

Parallel circuit voltage is easy to determine because it is the same across each resistor and/or load. The illustration shows a parallel circuit with voltmeters indicating the voltage across each resistor to be the same as the source battery.