Q. Two resistors are connected (a) in series (b) in parallel. The equivalent resistance in the two cases are $9\ ohm$ and $2\ ohm$ respectively. Then the resistance of the component resistors are
A) $2\ ohm$ and $7\ ohm$
B) $3\ ohm$ and $6\ ohm$
C) $3\ ohm$ and $9\ ohm$
D) $5\ ohm$ and $4\ ohm$
Explanation
(b) $R_{1} + R_{2} = 9$ and $\frac{R_{1}R_{2}}{R_{1} + R_{2}} = 2 \Rightarrow R_{1}R_{2} = 18$
$R_{1} - R_{2} = \sqrt{\left( R_{1} + R_{2} \right)^{2} - 4R_{1}R_{2}} = \sqrt{81 - 72} = 3$
$R_{1} = 6\Omega,\ R_{2} = 3\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.