Q. Two uniform wires $A$ and $B$ are of the same metal and have equal masses. The radius of wire $A$ is twice that of wire $B.$ The total resistance of $A$ and $B$ when connected in parallel is
A) $4\ \Omega$ when the resistance of wire $A$ is $4.25\ \Omega$
B) $5\ \Omega$ when the resistance of wire $A$ is $4.25\ \Omega$
C) $4\ \Omega$ when the resistance of wire $B$ is $4.25\ \Omega$
D) $5\ \Omega$ when the resistance of wire $B$ is $4.25\ \Omega$
Explanation
(a) $\frac{R_{A}}{R_{B}} = \left( \frac{r_{B}}{r_{A}} \right)^{4} \Rightarrow \frac{R_{A}}{R_{B}} = \left( \frac{1}{2} \right)^{4} = \frac{1}{16} \Rightarrow R_{B} = 16R_{A}$
When $R_{A}$ and $R_{B}$ are connected in parallel then equivalent resistance
$R_{eq} = \frac{R_{A}R_{B}}{(R_{A} + R_{B})} = \frac{16}{17}R_{A}$
If $R_{A} = 4.25\Omega$ then $R_{eq} = 4\Omega\ i.e.$ option (a) is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.