Math Snap

STEP 1

1. The temperature coefficient of resistance ($\alpha$) is a measure of how much the resistance of a material changes with temperature.
2. The formula for the temperature coefficient of resistance is given by:
$$ \alpha = \frac{1}{R_0} \cdot \frac{R - R_0}{T - T_0}
\] where $R_0$ is the resistance at the reference temperature $T_0$, and $R$ is the resistance at temperature $T$.
3. The inferred zero resistance temperature is the temperature at which the resistance is theoretically zero.

STEP 2

1. Identify the known values and the formula to use.
2. Substitute the known values into the formula.
3. Solve for the temperature coefficient of resistance ($\alpha$).

STEP 3

Identify the known values and the formula to use.
- The reference temperature $T_0 = 20^{\circ} \mathrm{C}$.
- The inferred zero resistance temperature $T = -162^{\circ} \mathrm{C}$.
- The formula to use is:
$$ \alpha = \frac{1}{T_0 - T}
\]

STEP 4

Substitute the known values into the formula.
Substitute $T_0 = 20^{\circ} \mathrm{C}$ and $T = -162^{\circ} \mathrm{C}$ into the formula:
$$\alpha = \frac{1}{20 - (-162)}$$

Solve for the temperature coefficient of resistance ($\alpha$).
Simplify the expression:
$$\alpha = \frac{1}{20 + 162}$$ $$\alpha = \frac{1}{182}$$ Calculate the value:
$$\alpha \approx 0.00549 /{ }^{\circ} \mathrm{C}$$ The temperature coefficient of resistance of iron at $20^{\circ} \mathrm{C}$ is approximately $0.00549 /{ }^{\circ} \mathrm{C}$.
Note: The provided answer $0.00551 /{ }^{\circ} \mathrm{C}$ might be due to rounding differences.