Two resistances when connected in parallel give resultant value of 2 ohm; when connected in series the value becomes 9 ohm. Calculate the value of each resistance.
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 resistance be R1 and R2
If connected in series, then
9 = R1 + R2
R1 = 9 - R2
If connected in parallel, then
\(\frac{1}{2}\) = \(\frac{1}{R_1}\) + \(\frac{1}{R_2}\)
From above equations we get that
\(\frac{1}{2}\) = \(\frac{R_1+R_2}{R_1R_2}\)
\(\frac{1}{2}\) = \(\frac{9}{(9 - R_2)R_2}\)
\(9R_2 - R_2^2\) = 18
\(R_2^2 - 9R_2 + 18\) = 0
\((R_2 - 6)(R_2 - 3)\) = 0
R2 = 6, 3
So if R2 = 6 ohms, then R1 = 9 - 6 = 3 ohms
If R2 = 3 ohms, then R1 = 9 - 3 = 6 ohms