Instructions

Remove insulation from the cable cores. Using a caliper, or preferably a micrometer (this will allow for a more accurate measurement), find the diameter of the core. You will get the value in millimeters. Then calculate the area cross section. To do this, multiply the coefficient 0.25 by the number π≈3.14 and the value of the diameter d squared S=0.25∙π∙d². Multiply this value by the number of cable cores. Knowing the length of the wire, its cross-section and the material from which it is made, calculate its resistance.

For example, if you need to find the cross-section of a copper cable with 4 cores, and the measurement of the core diameter gives a value of 2 mm, find its cross-sectional area. To do this, calculate the cross-sectional area of one core. It will be equal to S=0.25∙3.14∙2²=3.14 mm². Then determine the cross-section of the entire cable for this cross-section of one core, multiply by their number in our example it is 3.14∙4=12.56 mm².

Now you can find out the maximum current that can flow through it, or its resistance if the length is known. Calculate the maximum current for a copper cable from the ratio of 8 A per 1 mm². Then the maximum value of the current that can pass through the cable taken in the example is 8∙12.56 = 100.5 A. Keep in mind that for this ratio it is 5 A per 1 mm².

For example, the cable length is 200 m. To find its resistance, multiply resistivity copper ρ in Ohm∙mm²/m, by the cable length l and divide by its cross-sectional area S (R=ρ∙l/S). Having made the substitution, you will get R=0.0175∙200/12.56≈0.279 Ohm, which will lead to very small losses of electricity when transmitting it through such a cable.

Sources:

how to find out the cable cross-section

If a variable, sequence or function has infinite number values that change according to some law, it can tend to o to the limit number, which is the limit sequences. You can calculate limits different ways.

You will need

- concept number sequence and functions;
- ability to take derivatives;
- ability to transform and shorten expressions;
- calculator.

Instructions

To calculate the limit, substitute the limit value of the argument into its expression. Try the calculation. If this is possible, then the value with the substituted value is the desired one. Example: Find the limit values with common member(3 x?-2)/(2 x?+7), if x > 3. Substitute the limit into the expression sequences (3 3?-2)/(2 3?+7)=(27-2)/(18+7)=1.

If there is uncertainty when trying to substitute, choose a way to resolve it. This can be done by transforming the expressions in which . Having made the reductions, you will get the result. Example: Sequence (x+vx)/(x-vx), when x > 0. Direct substitution results in uncertainty 0/0. Get rid of it by taking it out of the numerator and denominator common multiplier. IN in this case it will be vx. Get (vx (vx+1))/(vx (vx-1))= (vx+1)/(vx-1). Now the substitution field will get 1/(-1)=-1.

When it is impossible to reduce due to uncertainty (especially if the sequence contains irrational expressions) multiply its numerator and denominator by the conjugate expression in order to remove it from the denominator. Example: Sequence x/(v(x+1)-1). The value of the variable x > 0. Multiply the numerator and denominator by the conjugate expression (v(x+1)+1). Get (x (v(x+1)+1))/((v(x+1)-1) (v(x+1)+1))=(x (v(x+1)+1) )/(x+1-1)= (x (v(x+1)+1))/x=v(x+1)+1. After substitution, you get =v(0+1)+1=1+1=2.

For uncertainties like 0/0 or?/? use L'Hopital's rule. For this, the numerator and denominator sequences imagine as functions, take from them . The limit of their relationship will be equal to the limit relations between the functions themselves. Example: Find the limit sequences ln(x)/vx, for x > ?. Direct substitution gives uncertainty?/?. Take the derivatives of the numerator and denominator and get (1/x)/(1/2 vx)=2/vx=0.

To reveal uncertainties, use the first wonderful limit sin(x)/x=1 for x>0, or the second wonderful limit (1+1/x)^x=exp for x>?. Example: Find the limit sequences sin(5 x)/(3 x) for x>0. Transform the expression sin(5 x)/(3/5 5 x) multiply the denominator 5/3 (sin(5 x)/(5 x)) using the first limit you get 5/3 1=5/3.

Example: Find the limit (1+1/(5 x))^(6 x) for x>?. Multiply and divide powers by 5 x. Get the expression ((1+1/(5 x))^(5 x)) ^(6 x)/(5 x). Applying the rule of the second wonderful limit, get exp^(6 x)/(5 x)=exp.

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Tip 9: How to find area axial section truncated cone

To solve this task, you need to remember what a truncated cone is and what properties it has. Be sure to make a drawing. This will allow you to determine what geometric figure the section represents. It is quite possible that after this, solving the problem will no longer be difficult for you.

Instructions

A round cone is a body obtained by rotating a triangle around one of its legs. Straight lines emanating from the apex cone and intersecting its base are called generators. If all generators are equal, then the cone is straight. At the base of the round cone lies a circle. The perpendicular dropped to the base from the vertex is the height cone. At the round straight cone the height coincides with its axis. The axis is a straight line connecting to the center of the base. If the horizontal cutting plane of a circular cone, then its upper base is a circle.

Since it is not specified in the problem statement that it is the cone that is given in this case, we can conclude that this is a straight truncated cone, the horizontal section of which is parallel to the base. Its axial section, i.e. vertical plane, which through the axis of the round cone, is an equilateral trapezoid. All axial sections round straight cone are equal to each other. Therefore, to find square axial sections, you need to find square trapezoid, the bases of which are the diameters of the bases of a truncated cone, A sides- its constituents. Frustum height cone is also the height of the trapezoid.

The area of a trapezoid is determined by the formula: S = ½(a+b) h, where S – square trapezoid; a – the size of the lower base of the trapezoid; b – the size of its upper base; h – the height of the trapezoid.

Since the condition does not specify which ones are given, it is possible that the diameters of both bases of the truncated cone known: AD = d1 – diameter of the lower base of the truncated cone;BC = d2 – diameter of its upper base; EH = h1 – height cone.Thus, square axial sections truncated cone is defined: S1 = ½ (d1+d2) h1

Sources:

area of a truncated cone

The regulatory documents for the design of electrical networks indicate the cross-sections of the wires, but only the cores can be measured with a caliper. These quantities are interrelated and can be converted from one to another.

Instructions

To convert the specified to regulatory document section single-core wire in its diameter, use the following formula: D=2sqrt(S/π), where D is diameter, mm; S - conductor cross-section, mm2 (electricians call it “squares”).

A flexible stranded wire consists of many thin strands twisted together and placed in a common insulating sheath. This allows it not to break during frequent movements, which is connected to the source with its help. To find the diameter of one core of such a conductor (this is what can be measured with a caliper), first find the cross-section of this core: s=S/n, where s is the cross-section of one core, mm2; S - total wire cross-section (indicated in the regulations); n is the number of cores. Then convert the core cross-section to diameter as indicated above.

Printed circuit boards use flat conductors. Instead of diameter, they have thickness and width. The first value is taken from the technical data of the foil material in advance. Knowing it, you can find the width by . To do this, use the following formula: W=S/h, where W is the conductor, mm; S - conductor cross-section, mm2; h - conductor thickness, mm.

Square conductors are relatively rare. Its cross-section must be converted either to a side or to the diagonal of a square (both can be measured with a caliper). sides is calculated as follows: L=sqrt(S), where L is side length, mm; S is the cross-section of the conductor, mm2. To find out the diagonal from the side length, make the following calculations: d=sqrt(2(L^2)), where d is the diagonal of the square, mm; L - side length, mm.

If there is no conductor whose cross-section exactly matches the required one, use another one with a larger, but in no case smaller, cross-section. Select the type of conductor and the type of its insulation depending on the conditions of use.

note

Before measuring the conductor with a caliper, remove the supply voltage and make sure there is no voltage using a voltmeter.

Sources:

diameter translation

For example, the diameter of the base of a straight cylinder is 8 cm, and its is 10 cm. Determine square its lateral surface. Calculate Radius cylinder. It is equal to R=8/2=4 cm. Generator of the straight line cylinder equal to its height, that is, L = 10 cm. For calculations, use a single formula, it is more convenient. Then S=2∙π∙R∙(R+L), substitute the corresponding numeric values S=2∙3.14∙4∙(4+10)=351.68 cm².

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Parallelogram is a quadrilateral whose sides are parallel in pairs.

In this figure opposite sides and the angles are equal to each other. The diagonals of a parallelogram intersect at one point and bisect it. Formulas for the area of a parallelogram allow you to find the value through the sides, height and diagonals. A parallelogram can also be presented in special cases. They are considered a rectangle, square and rhombus.
First, let's look at an example of calculating the area of a parallelogram by height and the side to which it is lowered.

This case is considered classic and does not require additional investigation. It’s better to consider the formula for calculating the area through two sides and the angle between them. The same method is used in calculations. If the sides and the angle between them are given, then the area is calculated as follows:

Suppose we are given a parallelogram with sides a = 4 cm, b = 6 cm. The angle between them is α = 30°. Let's find the area:

Area of a parallelogram through diagonals

The formula for the area of a parallelogram using the diagonals allows you to quickly find the value.
For calculations, you will need the size of the angle located between the diagonals.

Let's consider an example of calculating the area of a parallelogram using diagonals. Let a parallelogram be given with diagonals D = 7 cm, d = 5 cm. The angle between them is α = 30°. Let's substitute the data into the formula:

An example of calculating the area of a parallelogram through the diagonal was given to us great result – 8,75.

Knowing the formula for the area of a parallelogram through the diagonal, you can solve the set interesting tasks. Let's look at one of them.

Task: Given a parallelogram with an area of 92 square meters. see Point F is located in the middle of its side BC. Let's let's find the area trapezoid ADFB, which will lie in our parallelogram. First, let's draw everything we received according to the conditions.
Let's get to the solution:

According to our conditions, ah =92, and accordingly, the area of our trapezoid will be equal to

Square geometric figure - numerical characteristic a geometric figure showing the size of this figure (part of the surface limited by the closed contour of this figure). The size of the area is expressed by the number of square units contained in it.

Triangle area formulas

Formula for the area of a triangle by side and height
Area of a triangle equal to half the product of the length of a side of a triangle and the length of the altitude drawn to this side
Formula for the area of a triangle based on three sides and the radius of the circumcircle
Formula for the area of a triangle based on three sides and the radius of the inscribed circle
Area of a triangle is equal to the product of the semi-perimeter of the triangle and the radius of the inscribed circle.

Square area formulas

Formula for the area of a square by side length
Square area equal to the square of the length of its side.
Formula for the area of a square along the diagonal length
Square area equal to half the square of the length of its diagonal.
S= 1 2
2

Rectangle area formula

Area of a rectangle

Parallelogram area formulas

Formula for the area of a parallelogram based on side length and height
Area of a parallelogram
Formula for the area of a parallelogram based on two sides and the angle between them
Area of a parallelogram is equal to the product of the lengths of its sides multiplied by the sine of the angle between them.
a b sin α

Formulas for the area of a rhombus

Formula for the area of a rhombus based on side length and height
Area of a rhombus is equal to the product of the length of its side and the length of the height lowered to this side.
Formula for the area of a rhombus based on side length and angle
Area of a rhombus is equal to the product of the square of the length of its side and the sine of the angle between the sides of the rhombus.
Formula for the area of a rhombus based on the lengths of its diagonals
Area of a rhombus equal to half the product of the lengths of its diagonals.

Trapezoid area formulas

Heron's formula for trapezoid
Where S is the area of the trapezoid,
- lengths of the bases of the trapezoid,
- lengths of the sides of the trapezoid,

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