If there are two resistors r1 and r2 in a parallel circuit. r2 is 15 ohms greater than r1 and R=4 ohms calculate r1 and r2.

For resistances in parallel the equivalent resistance of
two resistors r1 and r2 is given as the reciprocal of the sum of their
inverses.

Or if the equivalent resistance is R. 1/R = 1/r1
+ 1/r2.

Now it is given that r2 = 15 greater than r1 or 15
+ r1.

Also the equivalent resistance R =
4

=> 1/4 = 1/ r1 + 1/(15 +
r1)

=> 1/4 = (15 + r1 + r1) / [r1
*(15+r1)]

=> [r1 *(15+r1)] = 4*(2*r1 +
15)

=> [r1 *(15+r1)] = 8 r1 +
60

=> 15r1 + r1^2 = 8r1 +
60

=> r1^2 + 7r1 - 60
=0

=> r1^2 + 12r1 - 5 r1 -
60=0

=> r1( r1+12) - 5(r1-
12)=0

=> (r1 -5)(r1+12)
=0

r1 can be -12 or 5

Now a
resistance cannot be negative. Therefore r1= 5.

r2 = 5+ 15
= 20

So the resistance r1 is 5 ohms and r2 is 20
ohms.

The required result is 5 ohms and 20
ohms