Question

Three unequal resistances are connected in parallel. Two of these resistances are in the ratio $1:2$. The equivalent resistance of these three connected in parallel is $1\Omega$. What is the highest resistance value among these three resistances if no resistance is fractional?

• A. $10\Omega$
• B. $8\Omega$
• C. $15\Omega$
• D. $6\Omega$

Answer 1

The correct option is D $6\Omega$

Let the resistance of first resistor be $x$ i.e. $R_1=x$
Resistance of second resistor $R_2=2x$
Let the third resistance be $y$ i.e $R_3=y$
Equivalent resistance $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$
$\therefore$ $\frac{1}{1}=\frac{1}{x}+\frac{1}{2x}+\frac{1}{y}$
$⟹y=\frac{2x}{2x-3}$
For $x=3$
We get $y=\frac{2\times 3}{(2\times 3-3)}=2$
Thus $R_1=3\Omega$, $R_2=6\Omega$ and $R_3=2\Omega$
Hence correct ansswer is $6\Omega$