Question

The resistance \( R \) of a conductor varies with temperature \( t \) as shown in the figure. If the variation is represented by \( R_t = R_0 \left( 1 + \alpha t + \beta t^2 \right) \), then:

• A. \( \alpha \) is positive and \( \beta \) is negative
• B. \( \alpha \) is negative and \( \beta \) is positive
• C. \( \alpha \) and \( \beta \) are both positive
• D. \( \alpha \) is negative and \( \beta \) is negative

Hint:

In temperature-dependent resistance equations, a positive \( \alpha \) and \( \beta \) indicate that resistance increases with temperature.

Answer 1

The Correct Option is C

From the graph, the resistance increases with temperature.
The given equation \( R_t = R_0 \left( 1 + \alpha t + \beta t^2 \right) \) represents the variation of resistance with temperature.
For the resistance to increase with temperature, the first coefficient \( \alpha \) must be positive because the linear term \( \alpha t \) contributes positively as \( t \) increases.
The second term \( \beta t^2 \) contributes in a similar manner.
Since the graph shows that the resistance increases more rapidly with higher temperatures, \( \beta \) must also be positive. Thus, both \( \alpha \) and \( \beta \) are positive. Therefore, the correct answer is (c).