Question

Derive the relation for equivalent resistance when three resistance are connected in parallel.

CBSE Class X Science SA 2 (3 Marks)

Answer 1

It is observed that the total current, I is equal to the sum of the separate currents through each branch of the combination.

Let R,be the equivalent resistance of the parallel combination of resistors. By applying Ohm's law to the parallel combination of resistors, we have,

1 = V/Rp

On applying Ohm's law to each resistor, we have

= V/RI; 12 = V/R2; and 13 = V/R3                                                  

From equations, we have

V/Rp=V/Ri + V/R2 + V/R3                                                          

OT 1/Rp=1/R1 +1/R2+1/R3 Vi Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

For the diagram, open the attachment.