Wed June 22, 2011 By:

Explain with the help of diagramto find resistence of of a combination of three resistors of resistence R1,R2,R3 joined in parallel.

Expert Reply
Wed June 22, 2011

For the equivalent resistance of resistors in parallel, an equivalent resistor R can replace the parallel combination of R1, R2 and R3 such that the voltage Vab is unchanged and the current through R is the total that would be drawn by R1, R2 and R3 in combination.

Thus for R,

V = I R

For R1, R2 and R3

V = IR1 R1
V = IR2 R2

V = IR3 R3

The can be found out to be

I = V/R
IR1 = V/R1
IR2 = V/R2

IR3 = V/R3

 But we know that for the equivalent resistor R the current draw is the sum of the currents drawn by R1, R2, and R3,

I = IR1 + IR2 + IR3
V/R = V/R1 + V/R2 + V/R3

Or 1/R = 1/R1 + 1/R2+ 1/R3

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