Deduce the expression for the equivalent resistance of three resistors connected in parallel.

The parallel combination of resistors: If a number of resistors are connected in between two common points so that each of them provides a separate path for current, then they are said to be connected in parallel.

As shown in the figure, consider three resistors R₁, R₂, R₃ connected in parallel.

Suppose a current I flows through the circuit when a cell of voltage V is connected across the combination. The current I at point A is divided into three parts I₁, I₂, I₃ through the resistors R₁, R₂, R₃ respectively. These three parts recombine at point B to give the same current I.

∴ I = I₁ + I₂ + I₃

As all the three resistors have been connected between the same two points A and B, voltage V across each of them is same. By Ohm’s law,

If R_P be the equivalent resistance of parallel combination, then,