a Coper wire with wire with a diameter of 1.5mm is joined to an alluminium wire, which has a diameter of 2.3mm. The wire carries a current of 1.2A. What is the current density in each wire?
Assuming that they are in series, 1.2 amps goes through each
so
current density = 1.2 /(pi d^2/4)
for each
To determine the current density in each wire, you need to know the cross-sectional area of each wire. The current density (J) is defined as the ratio of the current (I) to the cross-sectional area (A) of the wire:
J = I/A
To calculate the cross-sectional area, you need to use the formula for the area of a circle:
A = πr^2
Where A is the area, and r is the radius of the circle. Since the diameter (d) is given, you first need to find the radius (r) by dividing the diameter by 2.
Let's calculate the current density for each wire step by step:
For the copper wire:
1. Calculate the radius (r) by dividing the diameter (1.5 mm) by 2: r = 1.5 mm / 2 = 0.75 mm = 0.00075 m
2. Calculate the cross-sectional area (A) of the copper wire using the formula A = πr^2: A = π(0.00075 m)^2 = 0.001767 m^2
3. Calculate the current density (J) by dividing the current (1.2 A) by the cross-sectional area: J_copper = 1.2 A / 0.001767 m^2 ≈ 678.7 A/m^2
For the aluminum wire:
1. Calculate the radius (r) by dividing the diameter (2.3 mm) by 2: r = 2.3 mm / 2 = 1.15 mm = 0.00115 m
2. Calculate the cross-sectional area (A) of the aluminum wire using the formula A = πr^2: A = π(0.00115 m)^2 = 0.004155 m^2
3. Calculate the current density (J) by dividing the current (1.2 A) by the cross-sectional area: J_aluminum = 1.2 A / 0.004155 m^2 ≈ 288.8 A/m^2
So, the current density in the copper wire is approximately 678.7 A/m^2, and the current density in the aluminum wire is approximately 288.8 A/m^2.