Combination of Resistances in Parallel

Combination of Resistances in Parallel

Resistance in a conductor can be defined as the opposition offered to the flow of electrons. Resistance can be joined to each other in two ways:

Parallel Combination: If the resistances are connected between the same two points such that the potential drop across each resistance is same, then the resistances are said to be in parallel as shown in the below figure.

Parallel Combination

In this case, if V is the potential difference between the point A and B, then:

V = i₁ R₁; V = i₂ R₂; V = i₃ R₃

i₁ = V/ R₁; i₂ = V/ R₂; i₃ = V/ R₃

Therefore, the total current flowing through the battery is:

i = i₁ + i₂ + i₃ = V/ R₁ + V/ R₂ + V/ R₃

i = V (1/ R₁ + 1/ R₂ + 1/ R₃)

Parallel Combination 1

Also by Ohm’s Law, i = V/R, where R is the equivalent resistance between A and B. So we get:

1/ R = (1/ R₁ + 1/ R₂ + 1/ R₃).