Effective or equivalent resistance in series and parallel circuitsCopy

Learning Objectives

• Understand that the current at every point in a series circuit is the same
• Calculate the combined e.m.f. of several sources in series
• Give the combined resistance of two or more resistors in series
• Recall and use the fact that the sum of the p.d.s across the components in a series circuit is equal to the total p.d. across the supply
• State that, for a parallel circuit, the current from the source is larger than the current in each branch
• Recall and use the fact that the current from the source is the sum of the currents in the separate branches of a parallel circuit
• State that the combined resistance of two resistors in parallel is less than that of either resistor by itself
• State the advantages of connecting lamps in parallel in a lighting circuit
• Calculate the effective resistance of two resistors in parallel

Contents to learn

Effective or equivalent resistance in series circuits
Effective or equivalent resistance in series circuit can be calculated by simply adding all the resistance connected in series.

If R1, R2 and R3 are connected in series, then their effective or equivalent resistance can be calculated as

R = R1 + R2 + R3

Note: Effective or equivalent resistance in series circuit is always greater than the greatest resistance present in the series

Effectice or equivalent resistance in parallel circuits
The effective or equivalent resistance of the parallel circuit can be calculated by using the following relation.

1/R = 1/R1 + 1/R2 + 1/R3 ——– (1)

Where R1, R2 and R3 are the resistors connected in parallel as shown below.

If only two resistors R1 and R2 are connected in parallel, then the simple form of the above realtion can be used as shown below.

R = R1R2 / R1 + R2 ——– (2)

Note: This simple realtion (2) is valid only for two resistors. For more than two resistors, you have to apply the above relation (1)

circuit.