Copper has $8.5 \times 10^{28}$ current carrying electrons per $\mathrm{m}^{3}$. A copper wire carries a current of $17 \mathrm{~mA}$, and the drift velocity of the electrons is measured to be $18 \times 10^{-6} \mathrm{~m} / \mathrm{s}$. What is the wire's radius?
A) $1.5 \mathrm{~mm}$
B) $0.15 \mathrm{~mm}$
C) $2.7 \mathrm{~mm}$
D) $0.27 \mathrm{~mm}$

Question

Quizplus · Accepted Answer

The current (I) carried by the wire can be expressed using the formula $I = nAve$, where $n$ is the number of charge carriers per unit volume, $A$ is the cross-sectional area of the wire, $v$ is the drift velocity, and $e$ is the charge of an electron ($1.6 \times 10^{-19} \mathrm{C}$). Given $I = 17 \mathrm{mA} = 17 \times 10^{-3} \mathrm{A}$, $n = 8.5 \times 10^{28} \mathrm{m}^{-3}$, and $v = 18 \times 10^{-6} \mathrm{m/s}$, we can solve for $A$ and then find the radius $r$ from $A = \pi r^2$. Rearranging the formula gives $A = \frac{I}{nve}$. Substituting the given values and solving for $r$ yields a radius of approximately $0.27 \mathrm{mm}$.

Copper Has 8.5×10288.5 \times 10^{28}8.5×1028 Current Carrying Electrons Per m3\mathrm{m}^{3}m3 a Copper Wire Carries a Current Of Per

Copper Has $8.5 \times 10^{28}$ Current Carrying Electrons Per $\mathrm{m}^{3}$ a Copper Wire Carries a Current Of Per