Grouping of Resistors

Two types of groupings of resistors are in common use. These are:

1. Series Grouping
2. Parallel Grouping

Equivalent resistance of the combination is defined as a single resistance which allows the same current to flow as the given combination when the same potential difference is applied across it.

Series Combination

You can connect many resistors in series by joining them end-to-end such that the same current passes through all the resistors.

V = V₁ + V₂

V = IR₁ + IR₂

V = I(R₁ + R₂)

V = IR_s

R_s = R₁ + R₂

The equivalent resistance of a series combination of resistors is equal to the sum of individual resistances.

Parallel Combination

You can connect the resistors in parallel by joining their one end at one point and the other ends at another point. In parallel combination, same potential difference exists across all resistors.

The main current divides into two parts.

I₁ = V/R₁

I₂ = V/R₂

I = I₁ + I₂

I = V(1/R₁ + 1/R₂)

I = V/R_p

1/R_p = 1/R₁ + 1/R₂

Reciprocal of equivalent resistance of parallel combination is equal to the sum of the reciprocals of individual resistances.

In homes, electrical appliances such as lamps, fans, heaters, etc. are connected in parallel and each has a separate switch. Potential difference across each remains the same and their working is not influenced by others. As you switch on bulbs and fans, the resistance of the electrical circuit of the house decreases and the current drawn from the mains goes on increasing.