Which of the following has the largest current flowing through it?
A)a 1-m long copper wire of diameter 1 mm connected to a battery of 10 V
B)a 0.5-m long copper wire of diameter 0.5 mm connected to a 5-V battery
C)a 2-m long copper wire of diameter 2 mm connected to a 20-V battery
D)a 1-m long copper wire of diameter 0.5 mm connected to a 5-V battery
E)All of the choices have the same current.

Question

Quizplus · Accepted Answer

The current flowing through a conductor is inversely proportional to its resistance, which depends on the material's resistivity, length, and cross-sectional area. The formula for resistance is $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity (constant for copper in all options), $L$ is the length, and $A$ is the cross-sectional area. The cross-sectional area of a wire is given by $A = \pi r^2$, where $r$ is the radius of the wire. For a given voltage, a lower resistance will result in a higher current according to Ohm's law ($I = \frac{V}{R}$). Option C has a larger diameter (thus a larger cross-sectional area, reducing resistance) and despite being longer, the effect of the larger area more significantly reduces its resistance compared to the others. Additionally, it's connected to a higher voltage source, which would increase the current through it. Therefore, despite the increased length, the combination of a significantly larger cross-sectional area and higher voltage in option C means it will have the largest current flowing through it.

Which of the Following Has the Largest Current Flowing Through