Question

When two resistors of unknown resistance are joined in parallel, the equivalent resistance is 2 ohm. When the same resistors are joined in series, the equivalent resistance is 9 ohm. What are the resistance of the two resistors?

Answer 1

Suppose the two resistances are $R_1$ and $R_2$.

According to question,

$\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{2}$

Or $\frac{R_1{R}_2}{R_1+R_2}=2$...................(i)

And $R_1+R_2=9$

Or $R_1=(9-R_2)$......................(ii)

Putting in (i),

$\frac{(9-R_2)R_2}{9}=2$

$(9-R_2)R_2=18$

Or $R_2^2-9R_2+18=0$

Or $(R_2-6)(R_2-3)=0$

Or $R_2=6\Omega$ or $3\Omega$.

For $R_2=6\Omega =>R_1=3\Omega$

For $R_2=3\Omega =>R_1=6\Omega$.