Question

u are given two resistances r1 and r2 by using them singly in series and the parallel u can obtain four resistance of 1.5 ohm 2 ohm 6 ohm 8 ohm find r1 and r2 value




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Answer 1

Step-by-step explanation:

or series resistances:

R1 + R2 = 4.5

R2 = 4.5 - R1

R1 = 4.5 - R2

For parallel resistances:

1/Rt = 1/ R1 + 1/R2

Rt = R1R2 / R1+R2

The equivalent resistance of R1 and R2 connected in parallel is the ratio of the product of R1 and R2 by the sum of R1 and R2. Since the sum is 4.5 ohms and the value of Rt is 1.0 ohm then R1R2 is also 4.5 ohms to obtain a ratio of 1. That is 4.5 / 4.5 = 1. So R1R2 = 4.5 and R1 = 4.5 / R2. In R1 + R2 = 4.5, R1 = 4.5 - R2 and since the two are equal we equate them as 4.5 / R2 = 4.5 – R2.

Solving for R2:

4.5 / R2 = 4.5 – R2 and multiplying both sides by R2,

4.5 * (R2 / R2) = R2 * (4.5 – R2)

4.5 = 4.5 R2 – R2^2

0 = 4.5R2 - R2^2 – 4.5

Solving for the Quadratic equation:

-R2^2 + 4.5R2 – 4.5 = 0 and the roots are 1.5 and 3.0

R2 = 1.5 ohms and R1 = 3.0 ohms.