Law of Combination of Resistance in Parallel

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'.

Resistors Connected in Parallel Energized by a Battery

Here the potential difference across R₁ and R₂ will be equal to that of the battery voltage. But the total current I flowing in the circuit branches as I₁ through R₁ and I₂ through R₂.

Since there cannot be accumulation of charges at any point

I = I₁+ I₂ ______(1)

Using ohm's law,

Applying the set of equations (2) in (1)

Sub Topics

Inference

Inference

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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 generalized for any ‘n’ number of 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 are to be connected in parallel.