When several resistances are connected in such a way that one terminal of all the resistances is joined at a common point A and the other terminals are joined at another common point B and the potential difference across each of the resistors remains the same, then this combination of resistances is called parallel combination of resistances.

Fig: Parallel Combination of Resistances

Three resistors R_{1}, R_{2} and R are connected in a parallel combination. In this case, the same potential difference V is maintained across the two terminals of the three resistors. Different amount of current is flowing through each of the resistors owing to their different values. The main current I of the circuit splits into three parts at the junction a and later recombine at the point b. Let I_{1}, I_{2} and I_{3} are the currents flowing through the resistances R_{1}, R_{2} and R_{3} respectively. Therefore, some of the currents I_{1}, I_{2} and I_{3} of parallel paths is equal to the current I at the junction a.

Therefore, *I = I _{1} + I_{2 }+ I_{3}*

Here, the potential difference between the two terminals being V, applying Ohm’s law we get,

**I _{1} = V/R_{1} , I_{2} = V/R_{2}, I_{3 }= V/R_{3}**

If instead of three resistances, n numbers of resistances are connected in parallel then the equivalent resistance R_{p} can be expressed as;

**1/R _{P} = 1/R_{1} + 1/R_{2} + 1/R_{3}**

That is, resistances connected in a parallel combination, the sum of the inverse of the individual resistances is equal to the inverse of the equivalent resistance.