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Electricity and Magnetism

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Moderate

Resistance of Thin Silver and Steel Wires

EANDM-QJYMAZ

An electric potential of $V_{\rm{Ag}} = 16.2 \text{ V}$ is place across a thin silver wire with a cylindrical cross-section whose radius is $r = 15.0 \: \mu\rm{m}$ and whose length is $l = 0.85 \text{ m}$. The resulting current through the wire is $I = 847 \text{ mA}$.

In a cost-saving measure, the silver is replaced with steel. The proportions of the wire are kept the same. The resistivity of silver is $\rho_{\rm{Ag}} = 1.59 \times 10^{-8} \: \Omega \cdot \rm{m}$ and the resistivity of steel is $\rho_{\rm{St}} = 7.20 \times 10^{-7} \: \Omega \cdot \rm{m}$.

What potential $V_{\rm{St}}$ must be placed across the steel wire to obtain the same current?

A

$V_{\rm{St}} = 358 \text{ mV}$

B

$V_{\rm{St}} = 734 \text{ V}$

C

$V_{\rm{St}} = 73.4 \text{ V}$

D

$V_{\rm{St}} = 3.58 \text{ V}$