Question

Two resistance when connected in parallel gine
resultant value of 2ohm when connected in series the
value becomes 9ohm calculate the value of each
​

Answer 1

Answer:

Let the resistance be R¹ and R²

in series

R¹+R²= 9ohms ......१

in parallel

1/R = 1/R¹+ 1/R²= R¹+R²/R¹R²

R= R¹R²/R¹+R² =2ohms .........२

put eq १ in eq२

2 = R¹R²/9

R¹R²=18 ....३

(a+b)² = (a-b)² + 4ab

( R¹+R² )²= ( R¹-R² )² + 4×R¹R²

put value eq १ and eq ३ in

( R¹+R² )²= ( R¹-R² )² + 4×R¹R²

9²= (R¹-R²)² + 72

(R¹-R²)² = 9

R¹-R² = √9 =3 .....४

form eq १ and ४

2R¹ = 12

R¹= 6

put R¹ again in eq१

6+R²= 9

R²= 3

hence the two resistance are 6 and 3 ohms respectively