Wednesday, April 13, 2011

Law of Combination of Resistors in Parallel

CBSE ADDA
Law of Combination of Resistors 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 energised by a battery
Here the potential difference across R1and R2 will be equal to battery voltage. But the total current I flowing in the circuit branches as I1through R1and I2 through R2.
Since there cannot be accumulation of charges at any point
I = I1+ I2 ______(1)
Using Ohm's law,
I=image______(2)
Substituting the above set of equations (2) in equation (1) we get
imageimage ______ (3)
Divide  equation (3) throughout by V we get
imageimage

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.
image

Inference

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.

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