Question

Compute the voltage drop along a 24-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 13-A current. The resistivity of copper is 1.68×10−8Ω⋅m.

Answer 1

Concepts and reason

The required concepts to solve the problem are Ohm’s law and resistance.

First, using the relation between resistivity, length and area of the wire find the resistance of the wire. Then, by substituting the resistance in the Ohm’s law equation, find the voltage drop across the wire.

Fundamentals

According to Ohm’s law, the potential difference between the points in a wire is proportional to the current passing through it. The proportionality constant is called the resistance of the wire.

Here, is the potential difference, is the current and is the resistance.

The resistivity of a material is defined as the resistance of a unit length of the wire with a unit cross-sectional area.

$R= $

Here, is the resistivity of the material, is the length of the wire, and is the area of cross-section.

The area of the wire is,

…… (1)

Here, is the radius.

The radius of the wire is,

Here, is the diameter of the copper wire.

Replace for r in the equation (1).

…… (2)

The equation for resistance is,

$R= $ …… (3)

Substitute equation (2) in equation (3).

Substitute for , for and for.

According to Ohm’s law, the equation for potential drop is,

Substitute for I and for R.

Ans:

The potential drop across the copper wire is .