Electricity

Connect two resistors 'R₁' and 'R₂' in parallel to one another between the points A and B. Connect this combination to a battery of potential 'V'.

Here the potential difference across R₁and R₂ will be equal to battery voltage. But the total current I flowing in the circuit branches as I₁ through R₁and I₂ through R₂.

Since there cannot be accumulation of charges at any point

I = I₁+ I₂ ______(1)

Using Ohm's law,

I=______(2)

Substituting the above set of equations (2) in equation (1) we get

______ (3)

Divide  equation (3) throughout by V we get

Inference

If the resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of all the individual resistances. This result can be generalised for any n resistors.

From the above derivations we find that if we want to increase the resistance we should connect them in series and if we want to decrease the resistance then the individual resistors should be connected in parallel, in the circuit.