Question

The resistance $R_t$ of a conductor varies with temperature $t$ as shown in the figure. If the variation is represented by
$R_t=R_0[1+\alpha t+\beta t^2],$ then

• A. $\alpha$ is negative and $\alpha$ are positive
  
• B. $\alpha$ is positive and $\beta$ is negative
  
• C. $\alpha$ and $\beta$ are both positive
  
• D. $\alpha$ and $\beta$ are both negative"
  

Answer 1

The correct option is C $\alpha$ and $\beta$ are both positive


Step 1: Variation of $R$

Variation of $R$ with temperature ($t$) is shown as


From the figure, it is clear that $R$ is increasing continuously with temperature.

Step 2: Signs of $\alpha$ and $\beta$

Given,

$R_t=R_0[1+\alpha t+\beta t^2]$


For $R$ to increase continuously $\alpha$ and $\beta$ both should be positive.

For every other option, $R$ will not increase continuously.

Hence, option (b) is correct.