Question

The I-V graph for a conductor at two different temperatures 100°C and 400°C is as shown in the figure. The temperature coefficient of resistance of the conductor is about (in per degree Celsius)

• A. 3×10^-3
• B. 6×10^-3
• C. 9×10^-3
• D. 12×10^-3

Answer 1

The Correct Option is A

Given:

• Temperatures: \( T_1 = 100^\circ C \), \( T_2 = 400^\circ C \)
• Graph gives angles of I–V line with horizontal (V-axis):
  • \( \theta_1 = 45^\circ \) at \( T_1 \)
  • \( \theta_2 = 30^\circ \) at \( T_2 \)

Step 1: Use Slope to Find Resistance

The slope of the I–V graph is \( \frac{I}{V} = \frac{1}{R} \), so:

\[ R = \frac{1}{\tan(\theta)} \]

At \( T_1 = 100^\circ C \),

\[ R_1 = \frac{1}{\tan(45^\circ)} = \frac{1}{1} = 1 \]

At \( T_2 = 400^\circ C \),

\[ R_2 = \frac{1}{\tan(30^\circ)} = \frac{1}{1/\sqrt{3}} = \sqrt{3} \approx 1.732 \]

Step 2: Use Temperature Coefficient Formula

The formula for temperature coefficient \( \alpha \) is:

\[ R = R_0 (1 + \alpha \Delta T) \Rightarrow \alpha = \frac{R_2 - R_1}{R_1 \cdot \Delta T} \]

Here,

\[ R_1 = 1,\quad R_2 = \sqrt{3},\quad \Delta T = 400^\circ C - 100^\circ C = 300^\circ C \] \[ \alpha = \frac{\sqrt{3} - 1}{1 \cdot 300} = \frac{1.732 - 1}{300} = \frac{0.732}{300} \approx 2.44 \times 10^{-3} \]

Rounded to the nearest given option, this is approximately:

\[{3 \times 10^{-3}} \, \text{per}^\circ C \]

Conclusion:

The temperature coefficient of resistance is approximately \( {3 \times 10^{-3}} \), so the correct answer is (A).