In this blog, us will evaluation the principle of resistance, resistivity and steps to calculate the minimum cross-sectional area and also diameter of any desired conductor.
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What is Resistance?
The residential or commercial property of a machine or a circuit the opposes the activity of current through it. Resistance is measure up in Ohms (Ω). The resistance of any kind of material v a uniform cross-sectional area is determined by the adhering to four factors:The kind of materialThe lengthThe cross-sectional areaThe temperature
What is Resistivity?
Resistivity is the measure of just how much a given size of details material resists the current flow. While materials resist electrical current flow, part are far better at conducting it than others. Resistivity is offered to to compare the natural resistance qualities of various materials. Materials that conveniently conduct existing are described as conductors. Conductors have actually a low resistivity. If the products that carry out not quickly conduct existing are referred to as insulators. Insulators have actually a high resistivity. The resistivity that a product plays vital role in selecting the products used for electrical wire.
Now the we understand the principle of resistance and also resistivity clearly, let’s evaluation the general relationship of an easy conductor resistance, which suggests that the resistance the a offered conductor is equal to the product resistivity time the ratio of its length to that is cross-sectional area. This can help us to calculation the minimum cross-sectional area and diameter of any kind of desired conductor.
Let’s work out an instance to understand the procedures to calculation the minimum cross-sectional area and also diameter of any type of desired conductor.
Example: What is the minimum cross-sectional area and also diameter the conductor because that a 750-meter-long copper wire having actually a best resistance that 0.2 ohms?
Minimum Cross-sectional Area:
To settle this problem, we will use the general relationship because that calculating conductor resistance utilizing the formula below:
Resistance = Resistivity * (Length / Area )
R = Resistance of material, in Ohms
Ρ = product Resistivity, in Ohms per meter
L = Conductor Length, in meters
A = Cross-sectional Area, in square meters
In stimulate to usage this basic relationship to fix our example problem, we need the specific resistance or resistivity the copper. Note that we get the resistivity the conductor products from the table that conductor resistivity and we understand now the copper has a resistivity that 1.72 x 10e-8 ohms per meter.
While fixing Conductor Resistance, remember come express resistance in ohms, material resistivity in ohms every meter, conductor size in meters, and also cross-sectional area in square meters because that this relationship to it is in valid. We can then move on to calculation the cross-sectional area that the cable by substituting for the recognized quantities in the example.
Diameter that the conductor:
Area the a circle can be stood for using listed below formula. Us will need to rearrange the formula to resolve for diameter.
We have the right to now instead of our obtained cross-sectional area worth from Eq. (1) right into this relationship and calculate the diameter that the copper cable to come at a diameter of 0.009062 meters.
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d = 4*0.00006453.1415920.5
d = (8.212395*10-5)0.5
d = 0.009062 m
Now that we have actually the solution values, we will convert them and express our final answer using the conventional units.
A = 0.0000645 m2 = 64.5 mm2
d = 0.009062 m = 9.062 mm
Thereby, us conclude the our copper wire must have a minimum cross-sectional area the no less than 64.5 mm^2 and also a diameter the no less than 9.062 mm.