Question

Two coils connect in series have a resistance of 18 ohm and when connected in parallel have a resistance 4 ohm find the value of individual resistance of coil

Answer 1

Let the two resistance X and Y.

In series,

X + Y = 18

And in parallel, 1/4 = 1/X +1/Y

Or 4 = X *Y / X+Y

Put Y= 18- X.

4 = X*18-X / X + 18-X

4 = 18x -X^2 / 18

Or 18*4 = 18X - X^2

Or X^2 - 18X + 72 = 0

Solving Quadratic equation we get either

X= 12 Or X= 6 .

If X=6 , Y= 12.

Hence the two resistances are 12 ohms and 6 ohms