The equivalent resistance of two resistors connected in series is ( 6 ) and their parallel equivalent resistance is ( 4 3 ) What are the values of resistances?

Step-by-step solution

Let the two resistances be R₁ and R₂ When they are connected in series, equivalent resistance, R_ s =6 ₁+R₂=6 (1) When they are connected in parallel, equivalent resistance, R_ p = 4 3 1 R_ p = 1 R₁ + 1 R₂ 1 R₁ + 1 R₂ = 3 4 (2) Solving Eq. (2), we get R₁+R₂ R₁ R₂ = 3 4 R₁ R₂= (R₁+R₂ ) 4 3 R₁ R₂=6 4 3 R, R₂=2 4=8 ( Using Eq. (1)) R₁ R₂=2 4=8 (3) From Eq. (1), we have R₂=6-R₁ R₁ (6-R₁ )=8 6 R₁-R₁²=8 R₁²-6 R₁+8=0R₁= 6 36-32 2 = 6 4 2 = 6 2 2 =4 or 2 Using Eq. (3), we get R₂=2 or 4 Therefore, the two resistances are 4