Question

The resistance of a wire at \(20^\circ C\) is \(20\Omega\) and at \(500^\circ C\) is \(60\Omega\). At which temperature its resistance will be \(25\Omega\)?

• A. \(50^\circ C\)
• B. \(60^\circ C\)
• C. \(70^\circ C\)
• D. \(80^\circ C\)

Hint:

Use ratio method for linear variation: \[ \frac{\Delta R}{\text{total change}} = \frac{\Delta T}{\text{total temperature range}} \]

Answer 1

The Correct Option is D

Concept: Resistance varies linearly with temperature: \[ \frac{R - R_1}{R_2 - R_1} = \frac{t - t_1}{t_2 - t_1} \]

Step 1:Substitute values.
\[ \frac{25 - 20}{60 - 20} = \frac{t - 20}{500 - 20} \] \[ \frac{5}{40} = \frac{t - 20}{480} \]

Step 2:Solve.
\[ \frac{1}{8} = \frac{t - 20}{480} \] \[ t - 20 = 60 \Rightarrow t = 80^\circ C \]