# Current density in wires connected in series

• CIERAcyanide
In summary, the problem involves two wires, A and B, with equal lengths of 40.0 m and equal diameters of 2.60 mm, connected in series. A potential difference of 60.0 V is applied across the composite wire, with resistances of 0.127 and 0.729 for wires A and B, respectively. To find the current density in each wire, the cross-sectional area of the wire is needed. The volume of one wire is found to be 2.124E-4, and the total resistance of the wires in series can be used to calculate the current.

## Homework Statement

Wires A and B, having equal lengths of 40.0 m and equal diameters of 2.60 mm, are connected in series. A potential difference of 60.0 V is applied between the ends of the composite wire. The resistances of the wires are 0.127 and 0.729 , respectively.

Determine:
(a) the current density in each wire [A/m2]

(b) the potential difference across each wire. [V]

V = iR

## The Attempt at a Solution

I found the volume of 1 wire, SA times Length, 2.6 mm diameter is a .0013 m radius, squared times pi yields 5.31 E-6 for the surface area, times the length of 40m is volume of 2.124E-4.
I tried V=iR, but for the first wire I had 60=.127R, which would make the current 472.44, which I'm not sure how to relate to the volume.
I don't know how to find the potential difference either.

CIERAcyanide said:

## The Attempt at a Solution

I found the volume of 1 wire, SA times Length, 2.6 mm diameter is a .0013 m radius, squared times pi yields 5.31 E-6 for the surface area,
That's actually the cross-sectional area, not the surface area.

...times the length of 40m is volume of 2.124E-4.
The volume is not needed here.
I tried V=iR, but for the first wire I had 60=.127R, which would make the current 472.44, which I'm not sure how to relate to the volume.
V is not 60V for either wire, it is 60V across the series combination of the two wires.

What is the total resistance of the two wires connected in series? You can use that to find the current.
I don't know how to find the potential difference either.
We'll worry about that later, let's get part (a) first.

## 1. What is current density?

Current density is a measure of the amount of electrical current flowing through a given area of a material. It is typically represented by the symbol J and is measured in amperes per square meter (A/m2).

## 2. How does current density change in wires connected in series?

When wires are connected in series, the current density remains constant throughout all of the wires. This means that the same amount of current is flowing through each wire, regardless of the wire's size or material.

## 3. Why is current density important in series circuits?

Current density is important in series circuits because it helps us understand how the current is distributed among the different components in the circuit. This information is useful in determining the resistance and power dissipation of each component.

## 4. How can current density be calculated in a series circuit?

To calculate the current density in a series circuit, you will need to know the total current flowing through the circuit and the cross-sectional area of each wire. Then, you can divide the total current by the sum of the cross-sectional areas of all the wires to get the current density.

## 5. What factors can affect current density in wires connected in series?

The main factors that can affect current density in wires connected in series are the total current flowing through the circuit, the resistance of each wire, and the cross-sectional area of each wire. Changes in any of these factors can result in a change in the current density.