Solution:

To find the temperature coefficient of resistance $\alpha$ of the conductor, we use the formula for the change in resistance with temperature:

$$R_T = R_0 \left( 1 + \alpha T \right)$$

Where:

• $R_T$ is the resistance at temperature $T$,
• $R_0$ is the resistance at the reference temperature (0°C),
• $\alpha$ is the temperature coefficient of resistance,
• $T$ is the temperature change in °C.

Step 1: Given

• The ratio of resistances at 15°C and 37.5°C is given as $\frac{R_{15}}{R_{37.5}} = \frac{4}{5}$.
• The resistance at temperature 15°C, $R_{15} = R_0 (1 + \alpha \times 15)$.
• The resistance at temperature 37.5°C, $R_{37.5} = R_0 (1 + \alpha \times 37.5)$.

Step 2: Set up the equation based on the given ratio

$$\frac{R_{15}}{R_{37.5}} = \frac{4}{5}$$

Substituting the expressions for $R_{15}$ and $R_{37.5}$:

$$\frac{R_0 (1 + \alpha \times 15)}{R_0 (1 + \alpha \times 37.5)} = \frac{4}{5}$$

Canceling $R_0$ from both the numerator and denominator:

$$\frac{1 + 15\alpha}{1 + 37.5\alpha} = \frac{4}{5}$$

Step 3: Solve for $\alpha$

Cross-multiply to solve for $\alpha$:

$$5(1 + 15\alpha) = 4(1 + 37.5\alpha)$$

Expanding both sides:

$$5 + 75\alpha = 4 + 150\alpha$$

Simplify:

$$5 - 4 = 150\alpha - 75\alpha$$ $$1 = 75\alpha$$ $$\alpha = \frac{1}{75}$$

Final Answer:

The temperature coefficient of resistance $\alpha$ is $\boxed{\frac{1}{75}} \, \text{per °C}$.

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Solution:

When two resistors with resistances $R_1$ and $R_2$

and temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ are connected in series, the effective temperature coefficient of resistance $\alpha_{\text{eff}}$

is given by the formula:

$$\alpha_{\text{eff}} = \frac{\alpha_1 R_1 + \alpha_2 R_2}{R_1 + R_2}$$

This formula takes into account the individual resistances and temperature coefficients of the two wires, considering that their total resistance is the sum of the individual resistances.

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Solution:

Slope of V-I graph represents Resistance. So R1>R2

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