27.3 : Resistors In Parallel

Resistors are in parallel when one end of all the resistors are connected to a continuous wire of negligible resistance and the other end of all the resistors are also connected to one another through a continuous wire of negligible resistance. In the case of a parallel configuration, the potential drop across each resistor is the same. Current through each resistor can be found using Ohm’s law, I = V/R, where the voltage is constant across each resistor. The sum of the individual currents equals the current that flows into the parallel connections.

The expression for equivalent resistance can be generalized for the n-number of resistors connected parallelly.

For any number of resistors in parallel, the reciprocal of the equivalent resistance equals the sum of the reciprocals of their individual resistances.

An automobile’s headlights and taillights, radio, and the wiring in a house or any building are examples of systems that are wired in parallel. The advantage of connecting a circuit in parallel combination is that each subsystem utilizes the total voltage of the source and can operate independently. If one component in the parallel circuit burns out, the others keep working.