Lesson 2. Reducing Parallel Circuits

Parallel circuits are reduced to a single resistor value by simply applying the parallel-resistance formula. The total resistance of a parallel circuit and its equivalent resistance are one and the same.

 Note So why are we giving a different name to a procedure that is essentially identical to finding the total resistance of a circuit? We are actually getting you ready for dealing with more complicated circuits. Once you see how to handle the procedures for equivalent resistance for simple and familiar circuits, you will be in a better position to handle the more complex versions that really do require special treatment.

Example 1

Determine the equivalent resistance, R1, 2, for this two-resistor parallel circuit:

Solution

This is a parallel combination, so:

R1, 2 = R1 || R2

Where:
R1  and R2 are the given values
R1, 2 = equivalent resistance of the circuit

 Note We use the || symbol here to indicate the inverse-sums formula for parallel resistance. For example: RT = R1 || R2 || R3 is the same as

Example 2

Determine the equivalent resistance, R1, 2, 3 for this three-resistor parallel circuit:

Solution

This is a  parallel combination, so:

R1, 2, 3 = R1 || R2 || R3

Where:
R1, R2, and R3 are the given values
R1, 2, 3 = equivalent resistance of the circuit