A hollow copper wire with an inner diameter of 0.60mm and an outer diameter of 1.8mm carries a current of 15A. What is the current density in the wire?
Well, well, well, aren't we getting into the nitty-gritty of electrical engineering? Alright, let's crunch some numbers here.
To find the current density, we need to know the cross-sectional area of the wire. Now, the inner diameter is given as 0.60mm, and the outer diameter is given as 1.8mm. So, first we need to find the radius of the wire.
The inner radius (r1) is half of the inner diameter, which is 0.30mm. And the outer radius (r2) is half of the outer diameter, which is 0.90mm. Got it so far?
Now, let's calculate the cross-sectional areas of the inner (A1) and outer (A2) surfaces of the wire using the formula for finding the area of a circle: A = π * r^2. Remember, we're dealing with radii, not diameters!
A1 = π * (0.30mm)^2
A2 = π * (0.90mm)^2
Alrighty, now that we have the cross-sectional areas, let's go ahead and calculate the current density (J) using the formula: J = I/A, where I is the current and A is the cross-sectional area.
J = 15A / (A2 - A1)
Plug in the values we've found and calculate away! Now, I'm not an electrical engineer, but I believe that should give you the current density in the wire.
To find the current density in the wire, we need to calculate the cross-sectional area of the wire first.
The inner radius of the wire can be calculated by dividing the inner diameter by 2:
Inner radius (r1) = inner diameter / 2 = 0.60mm / 2 = 0.30mm = 0.30 x 10^-3 m
The outer radius of the wire can be calculated using the same method:
Outer radius (r2) = outer diameter / 2 = 1.8mm / 2 = 0.90mm = 0.90 x 10^-3 m
Now, we can calculate the cross-sectional area of the wire:
Inner area (A1) = π * (r1)^2
Outer area (A2) = π * (r2)^2
The difference between the outer area and the inner area will give us the area of the copper material through which the current is passing:
Copper area (A) = A2 - A1
Substituting the values:
Copper area (A) = π * (0.90 x 10^-3 m)^2 - π * (0.30 x 10^-3 m)^2
Using the value of π (pi) as 3.14159:
Copper area (A) = 3.14159 * [(0.90 x 10^-3 m)^2 - (0.30 x 10^-3 m)^2]
Now, we can calculate the current density (J) using the formula:
Current density (J) = Current (I) / Copper area (A)
Substituting the values:
Current density (J) = 15 A / [3.14159 * [(0.90 x 10^-3 m)^2 - (0.30 x 10^-3 m)^2]]
Calculating this expression will give us the current density in the wire.
To find the current density in the wire, we first need to calculate the cross-sectional area of the wire. We can then divide the current by the cross-sectional area.
The cross-sectional area of the wire can be calculated by subtracting the area of the inner circle from the area of the outer circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
To find the radius of the inner circle, we divide the inner diameter by 2. Similarly, we divide the outer diameter by 2 to find the radius of the outer circle.
Inner radius (r1) = Inner diameter / 2 = 0.60mm / 2 = 0.30mm = 0.00030m
Outer radius (r2) = Outer diameter / 2 = 1.8mm / 2 = 0.90mm = 0.00090m
The area of the inner circle (A1) = πr1^2 = π(0.00030m)^2
The area of the outer circle (A2) = πr2^2 = π(0.00090m)^2
Now, subtracting the area of the inner circle from the area of the outer circle will give us the area of the copper wire:
Cross-sectional area (A) = A2 - A1
Next, we can calculate the current density by dividing the current (I) by the cross-sectional area (A):
Current density (J) = I / A
Now let's calculate the values step by step.
Inner radius (r1) = 0.00030m
Outer radius (r2) = 0.00090m
Area of the inner circle (A1) = π(0.00030m)^2
Area of the outer circle (A2) = π(0.00090m)^2
Cross-sectional area (A) = A2 - A1
Current (I) = 15A
Current density (J) = I / A
Now you can plug in the values and calculate the current density yourself.