Q. The resistance of a conductor is $5\ ohm$ at $50℃$ and $6\ ohm$ at $100℃$. Its resistance at $0℃$ is
A) $1\ ohm$
B) $2\ ohm$
C) $3\ ohm$
D) $4\ ohm$
Explanation
(d) $\frac{R_{1}}{R_{2}} = \frac{(1 + \alpha t_{1})}{(1 + \alpha t_{2})} \Rightarrow \frac{5}{6} = \frac{(1 + \alpha \times 50)}{(1 + \alpha \times 100)} \Rightarrow \alpha = \frac{1}{200}per\ ℃$
Again by $R_{t} = R_{0}(1 + \alpha t)$
$\Rightarrow 5 = R_{0}\left( 1 + \frac{1}{200} \times 50 \right) \Rightarrow R_{0} = 4\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.