Parallel Combination of Resistances or Parallel Resistances

In the parallel combination of resistances, we connect more than one resistance.  here, we connect more than one resistor in a certain manner.  We connect one end of all the resistors to a common node. Then we connect the other end of all resistors to another node. The picture below is showing a parallel connection of resistors.  

Resistances in Parallel

Suppose, we connect a source with a parallel combination of resistors.  The parallel resistances divide the source current through them according to the value of the individual resistances. The current through each resistance is inversely proportional to its resistance value.  

Parallel Resistances
Parallel Resistances

If the current from the source is I. The current flowing through resistance R1 is I1, through R2 is I2 and through R3 is I3.

Now we can write  

The voltage drop across the resistance R1 is R1I1, across resistance R2 is R2I2 and across R3 is R3I3.

Parallel Resistors

As these three resistors are in parallel, the voltage drop across each resistor is the same. Also, it equals the source voltage.

Let us consider the equivalent resistance of the parallel combination is R. As the source current is I, the voltage drop across the equivalent resistance would be RI. 

From the above equation, we can write the expression of equivalent resistance of the parallel resistors as follows.  

or

Instead of three, if there were n number of resistances in parallel, the equivalent resistance would be  

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