Question

when 2 resistors are joined in series the equivalent resistance is 90 ohms when same resistors are joined in parallel. the equivalent resistance is 20 ohms. calculate resistances of two resistors

Answer 1

so the resistors are of ( 30 & 60 )Ohm

Answer 2

Answer: 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

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