a copper wire with a diameter of 1.5mm is joined to an aluminium wire which has a diameter of 2.3mm.the wire carries a current of 12A.what is the current density in each wire
As I recall, current density is I/a, where I is the current, and a is the cross-sectional area. So, that makes it
12/(π/4 d^2) A/mm^2
where d is 1.5 or 2.3
I can just use one of them
One will be limiting
To calculate the current density in each wire, we need to know the area of each wire's cross-section.
The formula for calculating the area of a circle is A = πr², where A is the area and r is the radius of the circle.
For the copper wire:
Given diameter = 1.5mm
Radius (copper) = diameter/2 = 1.5mm/2 = 0.75mm = 0.75 × 10^(-3) m
For the aluminium wire:
Given diameter = 2.3mm
Radius (aluminium) = diameter/2 = 2.3mm/2 = 1.15mm = 1.15 × 10^(-3) m
Now, let's calculate the area of each wire:
Area (copper) = π(0.75 × 10^(-3))^2 = π(5.625 × 10^(-7)) ≈ 1.767 × 10^(-6) m²
Area (aluminium) = π(1.15 × 10^(-3))^2 = π(1.3225 × 10^(-6)) ≈ 4.319 × 10^(-6) m²
To calculate the current density, we use the formula:
Current density = Current (A) / Area (m²)
For the copper wire:
Current density (copper) = 12A / 1.767 × 10^(-6) m² ≈ 6,792,453 A/m²
For the aluminium wire:
Current density (aluminium) = 12A / 4.319 × 10^(-6) m² ≈ 2,778,117 A/m²
So, the current density in the copper wire is approximately 6,792,453 A/m², and the current density in the aluminium wire is approximately 2,778,117 A/m².