Question

what physical characteristic determines the power rating of a resistor? what is the smallest value of resistance that can be used across 10 v if the power dissipated is not to exceed 0.5 w?

Explanation:

Step1: Recall power - resistance - voltage formula

The power formula is $P=\frac{V^{2}}{R}$, where $P$ is power, $V$ is voltage and $R$ is resistance.

Step2: Rearrange the formula for resistance

We can rewrite the formula as $R = \frac{V^{2}}{P}$.

Step3: Substitute given values

Given $V = 10\ V$ and $P=0.5\ W$. Substitute these values into the formula: $R=\frac{(10)^{2}}{0.5}$.

Step4: Calculate the resistance

$R=\frac{100}{0.5}=200\ \Omega$.

Answer:

The physical characteristic that determines the power rating of a resistor is its ability to dissipate heat (size, material, surface - area to volume ratio etc. contribute to heat - dissipation ability). The smallest value of resistance is $200\ \Omega$.