Question

At what temperature the resistance of a conductor becomes 20% more than its resistance at \(27^\circ\) C? (The value of the temperature coefficient of resistance of the conductor is \(2.0 \times 10^{-4}\)/K.)

• A. 900 K
• B. 1100 K
• C. 1300 K
• D. 1450 K

Hint:

Use \(R = R_0[1+\alpha \Delta T]\) with \(R = 1.2R_0\).

Answer 1

The Correct Option is C

Step 1: Fractional change method:
A 20% rise means \(\Delta R / R_0 = 0.2\). The coefficient is defined as $\alpha = \dfrac{\Delta R}{R_0\,\Delta T}$.

Step 2: Solve for the rise:
Rearranging, $\Delta T = \dfrac{\Delta R/R_0}{\alpha} = \dfrac{0.2}{2.0\times10^{-4}}$. This is $1000$ K, since a change of 1 K equals a change of 1 degree Celsius.

Step 3: Add to the starting temperature:
The starting temperature is 27 degrees Celsius, that is 300 K. Adding the rise gives $300 + 1000 = 1300$ K.

Step 4: Match:
1300 K is the third printed option.

Final Answer:
The required temperature is 1300 K, option 3. \[ \boxed{1300\ \text{K}} \]