Question

1. Two resistors when connected in parallel give
the resultant resistance of 2 ohm; but when
connected in series the effective resistance
becomes 9 ohm. Calculate the value of each
resistance.​

Answer 1

Answer:

Two resistances when connected in series, resultant value is 9 ohms.

Two resistances when connected in parallel, resultant value is 2 ohms.

Let the two resistances be R1 and R2.

If connected in series, then

9 = R1 + R2

R1 = 9 - R2

If connected in parallel, then

1/2 = 1/R1 + 1/R2

From above equations we get that

1/2 = (R1 + R2)/R1R2

1/2 = 9/(9 - R2) R2

9R2 - R22 = 18

R22 - 9R2 + 18 = 0

(R2 - 6) (R2 - 3) = 0

R2 = 6,3

So if R2 = 6ohms, then R1 = 9 - 6 = 3 ohms.

If R2 = 3ohms, then R1 = 9 - 3 = 6ohms