Question

The temperature coefficient of resistance of a wire is 0.00125 °C\(^{-1}\). At 300 K, its resistance is 1 \(\Omega\). At what temperature the resistance of the wire will be 2 \(\Omega\)?

• A. 800 K
• B. 1100 K
• C. 600 K
• D. None of the above

Hint:

Temperature coefficient \(\alpha\) is usually given per °C.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
\(R_t = R_0(1 + \alpha \Delta t)\).
Step 2: Detailed Explanation:
\(2 = 1(1 + 0.00125 \times \Delta T)\)
\(1 + 0.00125\Delta T = 2\)
\(\Delta T = 1/0.00125 = 800\ \mathrm{K}\)
\(T = 300 + 800 = 1100\ \mathrm{K}\)
Step 3: Final Answer:
Temperature is 1100 K.