Q. Two resistance wires on joining in parallel the resultant resistance is $\frac{6}{5}\ ohms.$ One of the wire breaks, the effective resistance is $2\ ohms.$ The resistance of the broken wire is
A) $\frac{3}{5}\ ohm$
B) $2\ ohm$
C) $\frac{6}{5}\ ohm$
D) $3\ ohm$
Explanation
(d) Suppose resistance of wires are $R_{1}$ and $R_{2}$ then
$\frac{6}{5} = \frac{R_{1}R_{2}}{R_{1} + R_{2}}.$ If $R_{2}$ breaks then $R_{1} = 2\Omega$
Hence, $\frac{6}{5} = \frac{2 \times R_{2}}{2 + R_{2}} \Rightarrow R_{2} = 3\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.