The temperature coefficient of resistance of a wire is 0.00125
per`^@C`. At 300K, its resistance is 1 ohm. This resistance of the wire will be 2 ohm at.

Options

A. 1154K
B. 1100K
C. 1400K
D. 1127K

Explanation

To solve the problem, we will use the formula for the resistance of a conductor as a function of temperature:

\[ R = R_0 (1 + \alpha (T - T_0)) \]

Where:
- \( R \) is the resistance at temperature \( T \),
- \( R_0 \) is the resistance at a reference temperature \( T_0 \),
- \( \alpha \) is the temperature coefficient of resistance,
- \( T \) is the final temperature in degrees Celsius,
- \( T_0 \) is the reference temperature in degrees Celsius.

### Step-by-Step Solution:

1. **Identify the given values:**
- Temperature coefficient of resistance, \( \alpha = 0.00125 \, \text{per} \, ^\circ C \)
- Initial resistance, \( R_1 = 1 \, \Omega \) at \( T_1 = 300 \, K \) (which is \( 27 \, ^\circ C \))
- Final resistance, \( R_2 = 2 \, \Omega \)

2. **Convert the initial temperature to Celsius:**
\[ T_1 = 300 \, K - 273.15 = 26.85 \, ^\circ C \approx 27 \, ^\circ C \]

3. **Set up the equations for the resistances:**
- For the initial resistance:
\[ R_1 = R_0 (1 + \alpha (T_1 - 0)) \]
- For the final resistance:
\[ R_2 = R_0 (1 + \alpha (T_2 - 0)) \]

4. **Substituting the known values into the equations:**
- From the first equation:
\[ 1 = R_0 (1 + 0.00125 \times 27) \]
- Simplifying:
\[ 1 = R_0 (1 + 0.03375) \]
\[ 1 = R_0 \times 1.03375 \]
\[ R_0 = \frac{1}{1.03375} \approx 0.967 \, \Omega \]

5. **Now substitute \( R_0 \) into the second equation:**
\[ 2 = 0.967 (1 + 0.00125 T_2) \]

6. **Solving for \( T_2 \):**
- Rearranging:
\[ 2 = 0.967 + 0.00125 \times 0.967 T_2 \]
\[ 2 - 0.967 = 0.00125 \times 0.967 T_2 \]
\[ 1.033 = 0.00125 \times 0.967 T_2 \]
\[ T_2 = \frac{1.033}{0.00125 \times 0.967} \]
\[ T_2 \approx \frac{1.033}{0.00120875} \approx 854.2 \, ^\circ C \]

7. **Convert \( T_2 \) back to Kelvin:**
\[ T_2 = 854.2 + 273.15 \approx 1127.35 \, K \]

### Final Answer:
The resistance of the wire will be 2 ohms at approximately **1127 K**.