The temperature coefficient of resistance of a wire is 0.00125 per degree celsius. At 300K its resistance is 1 ohm. The resistance of the wire will be 2 ohm at following temperature:

• A. 1154K.
• B. 400K.
• C. 600K.
• D. 1400K.

To find the temperature at which the resistance of the wire becomes 2 ohms, we can use the formula for resistance change with temperature:

Resistance Formula

The formula is given by:

R_t = R_0 (1 + α(T - T_0))

Where:

• R_t = resistance at temperature T
• R_0 = initial resistance at temperature T_0
• α = temperature coefficient of resistance
• T = final temperature
• T_0 = initial temperature

Given Values

From the problem:

• α = 0.00125 per °C
• R_0 = 1 ohm at T_0 = 300K
• R_t = 2 ohms

Calculating the Temperature

We need to rearrange the formula to solve for T:

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

This simplifies to:

2 = 1 + 0.00125(T - 300)

Subtracting 1 from both sides gives:

1 = 0.00125(T - 300)

Now, divide both sides by 0.00125:

800 = T - 300

Adding 300 to both sides results in:

T = 1100K

Comparing with Options

The closest option to 1100K is:

• A. 1154K
• B. 400K
• C. 600K
• D. 1400K

Thus, the resistance of the wire will be 2 ohms at approximately 1154K.