Question

Three unequal resistance 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 three resisters are $R_1,R_2\&R_3$, and $R_2=2R_1$.

By using resistance formula for parallel combination and using the given value gives, $R_3=\frac{2R1}{2R_1-3}$.

Since $R_3$ is not fractional, let $R_3=n$, $n$ is positive integer.

Then, $R_1=\frac{3n}{2(n-1)}$, we need $R_1$ to be non fractional too, i.e., $n$ should divisible by $2$ and $3$ should be divisible by $n-1$. So, $n=2,4$, $R_1=3,2$.

Highest resitance will be $R_2=6\Omega$ for $R_1=3\Omega$.