Compute the voltage drop along a 21-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.
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This is Giancoli Answers with Mr. Dychko. To calculate the voltage, we'll take the current and multiply it by the resistance of the wire. So first, we need to find the resistance. Resistance is the resistivity of the material which is copper in this case and multiply it by the length of the wire divided by its cross-sectional area. The cross-sectional area is pi times the radius squared because it's a cylindrical wire. That's gonna be pi times half the diameter squared or pi d squared over four. Then we'll substitute that in for area. And when we divide by area, we can instead multiply by its reciprocal, and so we have resistances four times resistivity times length, divided by pi times d squared. So it's four times resistivity of copper, 1.68 tis 10 to the minus 8 ohm-meters, times the length of 21 meters, divided by pi times 1.628 times 10 to the minus three meters, diameter for a number of 14 copper wire, and we square that. We get 0.1694845 ohms, which we then multiply by the current of 12 amps and get about 2.0 volts, is the voltage across the length of this wire.
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