Calculating Total Current in Cylindrical Wire at 60 Hz

In summary, the formula for calculating total current in a cylindrical wire at 60 Hz is I = (2πfμr) * (V / ln(b/a)), where I is the total current, f is the frequency (60 Hz), μ is the permeability of the wire, r is the radius of the wire, V is the voltage, and a and b are the inner and outer radii of the wire. The value of μ for a specific wire can be determined by consulting a table or chart of magnetic properties for different materials, and may vary based on frequency and temperature. This formula is specifically for cylindrical wires and cannot be used for wires of any shape or size. 60 Hz is the standard frequency for alternating current
  • #1
AC
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I have a thick cylindrical wire that I make it 10 smaller pieces and the area remains constant. How do I find the toatal current at 60 Hz? given sigma, miou, and radious
I also need to find the total current for a given maximum current density that was given for the thick wire for AC. How to??
and same for DC?
thanks in advance
I am really stuck with this problem and problem 9.36 griffiths 3rd edition
anyone has suggestions?
thanks for the help
 
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  • #2
nobody knows?
 
  • #3


To calculate the total current in a cylindrical wire at 60 Hz, you will need to use the formula for total current, which is given by I = σAωE, where σ is the conductivity of the material, A is the cross-sectional area of the wire, ω is the angular frequency (2πf) and E is the electric field.

To find the total current, you will first need to calculate the electric field. This can be done using the formula E = V/d, where V is the voltage and d is the distance between the ends of the wire.

Once you have calculated the electric field, you can plug in the values of σ, A, ω, and E into the formula for total current to find the total current at 60 Hz.

To find the total current for a given maximum current density for AC, you can use the formula I = JmaxA, where Jmax is the maximum current density and A is the cross-sectional area of the wire. Simply plug in the values and you will get the total current.

For DC, the total current can be found by using Ohm's law, which states that I = V/R, where V is the voltage and R is the resistance of the wire. In this case, the resistance can be calculated using the formula R = ρl/A, where ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area. Once you have calculated the resistance, you can use Ohm's law to find the total current.

I hope this helps with your problem. If you are still stuck, I would suggest seeking help from a tutor or your instructor. They will be able to provide more specific guidance and help you understand the concepts better. Good luck with your studies!
 

Related to Calculating Total Current in Cylindrical Wire at 60 Hz

What is the formula for calculating total current in a cylindrical wire at 60 Hz?

The formula for calculating total current in a cylindrical wire at 60 Hz is I = (2πfμr) * (V / ln(b/a)), where I is the total current, f is the frequency (60 Hz), μ is the permeability of the wire, r is the radius of the wire, V is the voltage, and a and b are the inner and outer radii of the wire.

How do I determine the value of μ for a specific wire?

The value of μ for a specific wire can be determined by consulting a table or chart of magnetic properties for different materials. The value of μ may also vary depending on the frequency and temperature of the wire.

Can I use this formula for wires of any shape or size?

No, this formula is specifically for cylindrical wires. Different shapes and sizes of wires may require different formulas for calculating total current.

What is the significance of 60 Hz in this calculation?

60 Hz is the standard frequency for alternating current (AC) in most countries. This value is used in the formula as it represents the frequency at which the current is oscillating.

How accurate is this formula for calculating total current in a cylindrical wire at 60 Hz?

This formula is a simplified version of the more complex formula for calculating total current in a cylindrical wire. It provides a reasonably accurate estimation but may not account for all factors that could affect the actual current in the wire. It is best to use this formula as a guide and make adjustments as needed based on the specific characteristics of the wire being used.

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