Question

A 100 m long copper wire (resistivity 1.70x10-8Ωm) has diameter of 1.50 mm. If the current in the wire is 15 A, what is the potential difference between the ends of the wire?Group of answer choices8.00 V14.4 V23.2 V28.5 V34.0 V

Answer 1

The potential difference is 14.4 V.

Given data:

The length of wire is l=100 m.

The resistivity of the copper is ρ=1.70x10^-8 Ωm.

The diameter of wire is d=1.50 mm.

The current in the wire is I=15 A.

The resistance of the wire can be calculated as,

`\begin{gathered} R=\rho(L)/(A) \\ R=\rho(L)/((\pi)/(4)d^2) \\ R=(1.7*10^(-8))(100)/((\pi)/(4)(1.5*10^(-3))^2) \\ R=0.962\text{ }\Omega \end{gathered}`

The potential difference can be calculated using the Ohm's law,

`\begin{gathered} \Delta V=IR \\ \Delta V=(15)(0.962) \\ \Delta V=14.4\text{ V} \end{gathered}`

Thus, the potential difference is 14.4 V.