A $1.0 - \mathrm { m }$ length of nichrome wire has a radius of $0.50 \mathrm {~mm}$ and a resistivity of $1.0 \times 10 ^ { - 6 } \Omega \cdot \mathrm { m }$. When this wire carries a current of $0.50 \mathrm {~A}$, what is the voltage across its ends?
A) $1.6 \mathrm {~V}$
B) $0.0030 \mathrm {~V}$
C) $0.64 \mathrm {~V}$
D) $0.32 \mathrm {~V}$

Question

Quizplus · Accepted Answer

The voltage across the wire can be calculated using Ohm's law $V = IR$, where $I$ is the current and $R$ is the resistance. The resistance $R$ can be calculated using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area of the wire. The area $A$ of a wire with radius $r$ is $\pi r^2$. Substituting the given values, $R = 1.0 \times 10^{-6} \Omega \cdot m \times \frac{1.0 m}{\pi (0.50 \times 10^{-3} m)^2}$, and then calculating $V = IR$ gives $0.64 V$.

A 1.0−m1.0 - \mathrm { m }1.0−m Length of Nichrome Wire Has a Radius Of

A $1.0 - \mathrm { m }$ Length of Nichrome Wire Has a Radius Of