Question

Three unequal resistors in parallel are equivalent to a resistance $1\Omega$. If two of them are in the ratio $1:2$ and if no resistance value is fractional, the largest of the three resistances in $\Omega$ is:

• A. $4$
• B. $6$
• C. $8$
• D. $12$

Answer 1

Answer: (B)

$6$

Let $R_1,R_2,$ and $R_3$ be the three resistances connected in parallel.
$R_p$ is equivalent resistance in parallel combination.
Hence,
$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$
Let, $R_2=2R_3$
Therefore,
$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{2R_3}+\frac{1}{R_3}$

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{3}{2R_3}$
$R_p=1\Omega$ ; given

$\frac{1}{R_1}=1-\frac{3}{2R_3}$

$\therefore R_1=\frac{2R_3}{(2R_3-3)}$

If $R_3=3\Omega$, $R_1=2\Omega$ and $R_2=6\Omega$
$\therefore$ Largest resistance $=6\Omega$