A resistor is constructed of a carbon rod that has a uniform...

A resistor is constructed of a carbon rod that has a uniform cross-sectional area of $5.00 \mathrm{mm}^{2} .$ When a potential difference of $15.0 \mathrm{V}$ is applied across the ends of the rod, the rod carries a current of $4.00 \times 10^{-3} \mathrm{A}$. Find (a) the resistance of the rod and (b) the rod's length.

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Key Concepts

Resistivity and the Geometric Dependence of Resistance

The resistance of a uniform material is not only determined by its intrinsic resistivity but also by its physical dimensions. The relationship R = ?L/A shows that the resistance increases with the length of the material and decreases with a larger cross-sectional area. Resistivity is a material-specific property that describes how strongly a material opposes the flow of electric current.

Unit Conversion in Electrical Measurements

Accurate calculations in electrical physics require the use of consistent units. For instance, converting areas from mm² to m² is crucial when applying formulas such as R = ?L/A, which are based on SI units. This step ensures that the results are dimensionally correct and comparable across different measurements.

Ohm's Law

Ohm's Law is a fundamental principle in electricity which states that the voltage across a conductor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance (V = IR). This law allows one to calculate any one of voltage, current, or resistance when the other two quantities are known, making it essential for analyzing electrical circuits.

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