Four copper wires of equal length are connected in series....

Four copper wires of equal length are connected in series. Their cross-sectional areas are $1.00 \mathrm{cm}^{2}, 2.00 \mathrm{cm}^{2}$ $3.00 \mathrm{cm}^{2},$ and $5.00 \mathrm{cm}^{2} .$ A potential difference of $120 \mathrm{V}$ is applied across the combination. Determine the voltage across the $2.00-\mathrm{cm}^{2}$ wire.

Key Concepts

Voltage Division Principle

The voltage division principle states that in a series circuit, the voltage drop across a resistor is proportional to its resistance relative to the total resistance. This principle allows the calculation of individual voltage drops when the total voltage and resistances are known.

Effect of Cross-Sectional Area on Resistance

The cross-sectional area of a conductor directly affects its resistance: a larger area reduces resistance, while a smaller area increases it. This inversely proportional relationship, as seen in the formula R = ?L/A, is crucial when comparing wires with different areas even if they are made of the same material and have the same length.

Resistance in a Conductor

Resistance is a measure of how much a material opposes the flow of electric current. It depends on the material's resistivity, the conductor's length, and its cross-sectional area according to the formula R = ?L/A, where ? is the resistivity, L is the length, and A is the cross-sectional area.

Series Circuits

In a series circuit, components are connected end-to-end so that the same current flows through each element. The total resistance is the sum of the individual resistances, and the applied voltage is divided among the resistors based on their resistances.

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