Question

We have two resistance r1 and r2. Resistance value is 4.5 ohm when connected in series and 1 ohm when connected in parallel . Find r1 and r2​

Answer 1

Answer:

3/2=r1

3=r2

in series

r1+ r2=4.5

in parralel

1=1/r1+1/r2

by solving both we get answrt

Answer 2

(i) r1 and r2 in series. so, r1 + r2 = 4.5

(ii) r1 and r2 in parallel. so,

r1*r2/r1+r2 = 1

=> r1 * r2/4.5 = 1

=> r1 * r2 = 4.5

=> r1 * (r1 - 4.5) = 4.5

=> r1^2 - 4.5r1 - 4.5 = 0

=> r1 = (4.5±√(4.5^2 - 4*1*4.5))/2

=> r1 = (4.5±√(20.25-18))/2

=> r1 = (4.5±√2.15)/2

=> r1 = (4.5±1.5)/2

=> r1 = 3/2, 6/2

=> r1 = 1.5, 3

so r2 = 4.5 - 1.5 , 4.5 - 3

=> r2 = 3, 1.5