Question

When two resistors are joined in series the equivalent resistance is 90 ohms. When the same resistors are joined in parallel, the equivalent resistance is 20 ohms. Calculate the resistance of the two resistors.

Answer 1

let the two resistors be R1 and R2.so,R1 + R2 = 90. .....(i) and,(R1×R2)/R1 + R2 = 20R1 × R2 = 20 (R1 + R2)putting value of equation 1
   =20*90 = 1800
Convert this into a quadratic equation
Let R1 be α & R2 be β
Therefore, α β = 1800, α+β= 20
General form of quadratic eq. = x2 – x(α +β)+ α β
Substituting values we get the following eq.,
x2 – 20x + 1800
= x2 – 60x- 30x + 1800
= x(x-60) – 30(x-60)
=(x-30)(x-60)
(x-30), (x-60) are factors. Therefore zeroes are 30 & 60
Thus, α = R1= 30 ohms, β =R2 = 60 ohms
Keep on asking such questions

Answer 2

Answer:

The resistance of the two resistors is 30Ω and 60Ω.

Explanation:

Given, the equivalent resistance of the resistors when in series is 90Ω.

         the equivalent resistance of the resistors when in parallel is 20Ω.

       We know the expression for equivalent resistance in series is R₁ + R₂

and when in parallel is R₁R₂/(R₁ + R₂).

By multiplying both we get R₁R₂ = 1800.

this implies that R₂ = 1800/R₁. Now substituting this in series expression we obtain the following quadratic equation.

                    R₁² -90R₁ + 1800 = 0

By solving the above equation we obtain the required resistances as 30Ω and 60Ω.