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

To solve the problem of finding the temperature at which the resistance of the wire becomes 2 Ω, we employ the temperature dependence of resistance formula, given by:

\(R_t = R_0 (1 + \alpha (T - T_0))\)

where:

• \(R_t\) is the resistance at temperature \(T\).
• \(R_0\) is the original resistance at the reference temperature \(T_0\).
• \(\alpha\) is the temperature coefficient of resistance.
• \(T\) is the desired temperature.
• \(T_0\) is the original temperature.

Given values:

• \(\alpha = 0.00125\) °C^-1
• \(R_0 = 1 \, \Omega\) at \(T_0 = 300 \, \text{K}\)
• \(R_t = 2 \, \Omega\)

Substitute the known values into the formula:

\(2 = 1 \times (1 + 0.00125 \times (T - 300))\)

Rearrange and solve for \(T\):

1. \(2 = 1 + 0.00125 \times (T - 300)\)
2. Subtract 1 from both sides: \(1 = 0.00125 \times (T - 300)\)
3. Divide both sides by 0.00125: \(\frac{1}{0.00125} = T - 300\)
4. Calculate: \(800 = T - 300\)
5. Add 300 to both sides to isolate \(T\): \(T = 1100 \, \text{K}\)

Thus, the temperature at which the resistance of the wire is 2 Ω is 1100 K. This corresponds to the correct answer.

Therefore, the correct option is 1100 K.