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By Automathic

Tags: Ohm's Law, Ohm, Electronics, Resistance, Watt, Voltage,...

10

Posted: 2013-04-16
Ohm's Law
Ohm's Law
$$$I = {V \over R} \; or \; V = IR \; or \; R = {V \over I}$$$

Among the most practically useful mathematical formulas, Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.

Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship (see formula above) where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

More info can be found here: http://en.wikipedia.org/wiki/Ohms_Law



By PiThagoras

Tags: Relativity, Special Relativity, Einstein, Speed...

5

Posted: 2013-03-05
Mass-Energy Equivalence
Mass-Energy Equivalence
$$$E = mc^2$$$

Perhaps the most famous formula in existence, Einstein's Mass-Energy Equivalence Formula changed the way we look at the world. In physics — in particular, special and general relativity — mass-energy equivalence is the concept that the mass of a body is a measure of its energy content.

E = Energy
m = Mass
c = The Speed of Light in a Vacuum

More info can be found here: http://en.wikipedia.org/wiki/Mass-energy_equivalence



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By PiThagoras

Tags: Circle, Disk, Disc, Pi, Area, Surface Area

1

Posted: 2013-02-05
Area of a Disc
Area of a Disc
$$$Area = \pi r^2$$$

The area of a disc (the region inside a circle), often incorrectly called the area of a circle, is $$ \pi r^2 $$ when the circle has radius r. Here the symbol $$ \pi $$ (Greek letter pi) denotes, as usual, the constant ratio of the circumference of a circle to its diameter. It is easy to deduce the area of a disk from basic principles: the area of a regular polygon is half its apothem times its perimeter, and a regular polygon becomes a circle as the number of sides increase, so the area of a disc is half its radius times its circumference (i.e. $${1 \over 2} r * 2 \pi r $$ ).

More information can be found here: en.wikipedia.org/wiki/Areaofa_circle



By Per

Tags: Calculus

1

Posted: 2013-07-02
Derivative of a function
Derivative of a function
$$${dF (x) \over dx}=lim_{\epsilon \rightarrow 0} {F(x+\epsilon)-F(x)\over \epsilon}$$$

The derivative of a function $$F(x)$$ denotes the slop of the graph $$(F(x),x)$$. Lim denotes the limit where $$\epsilon$$ goes toward zero.



By Per

Tags: Euler

1

Posted: 2013-07-07
Euler's identity
Euler's identity
$$$e^{i \pi}+1=0$$$

This is one of the most famous equations in all of mathematics. Its especially nice since it involves a large number of different central objects such as 0, 1, i, $$pi$$, $$e$$. The identity can be proved using that any given exponential $$e^{ix}$$ can be written as $$ e^{ix}=cos x + i sin x $$ for some real number x.



By Nathaniel

Tags: Electronics, Resistors

1

Posted: 2016-08-22
Resistors in series
Resistors in series
$$${R_t} = {R_1} + {R_2} + {R_3}$$$

Formula for resistors in series where R1 is the resistance of the first resistor, R2 is the resistance of the second resistor, R3 is the resistance of the third resistor, and R t is the total of all the resistors in series



By Nathaniel

Tags: Electronics, Resistors

1

Posted: 2016-08-22
Resistors in parallel
Resistors in parallel
$$${1 \over R_t} = {1 \over R_1} + {1 \over R_2} + {1 \over R_3}$$$

Formula for resistors in parallel where R1 is the resistance of the first resistor, R2 is the resistance of the second resistor, R3 is the resistance of the third resistor, and R t is the total of all the resistors in parallel



By Nathaniel

Tags: Electronics, Inductors

1

Posted: 2016-08-22
Inductors in parallel
Inductors in parallel
$$${1 \over L_t} = {1 \over L_1} + {1 \over L_2} + {1 \over L_3}$$$

Formula for inductors in parallel where L1 is the inductance of the first inductor, L2 is the inductance of the second inductor, L3 is the inductance of the third inductor, and L t is the total of all the inductors in parallel



By Nathaniel

Tags: Electronics, power, law

1

Posted: 2016-08-22
Power law
Power law
$$$P = VI \; or \; P = {V^2 \over R} \; or \; P = I^2R \;$$$

Formula for calculating power consumption (in watts) of a circuit based on voltage, current, and resistance.

Where P = power in watts, V = voltage, I = current, and R = resistance.



By PiThagoras

Tags: Newton, Gravity, Gravitation, Law, Force, Mass,...

0

Posted: 2013-03-13
Law of Universal Gravitation
Law of Universal Gravitation
$$$F = G \; {m_1 m_2 \over r^2}$$$

Newton's law of universal gravitation states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

$$F$$ = the force between the masses $$G$$ = the gravitational constant $$m1$$= the first mass $$m2$$ = the second mass $$r$$ = distance between the centres of the masses.

More info can be found on Wikipedia: http://en.wikipedia.org/wiki/Newton'slawofuniversalgravitation



By PiThagoras

Tags: Newton, Force, Mass, Acceleration, Mechanics, Law

0

Posted: 2013-03-05
Newton's Second Law
Newton's Second Law
$$$F = ma$$$

The acceleration (a) of a body is parallel and directly proportional to the net force (F) acting on the body, is in the direction of the net force, and is inversely proportional to the mass (m) of the body, i.e., $$F = ma$$



By PiThagoras

Tags: Pythagoras, Pythagorean, Triangle, Geometry, Theorem,...

0

Posted: 2013-04-09
Pythagorean Theorem
Pythagorean Theorem
$$$a^2 + b^2 = c^2$$$

In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is the relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:

In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

In the above equation: C = The Hypotenuse of a right triangle A & B = Lengths of the other two sides.



By PiThagoras

Tags: Triangle, Area, Base, Height, 1/2, Easy

0

Posted: 2013-04-09
Area of a Triangle
Area of a Triangle
$$$Area = {1 \over 2} B * H$$$

Calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is show above. The term Base denotes any side, and Height denotes the length of a perpendicular from the vertex opposite the side onto the line containing the side itself. Although simple, this formula is only useful if the height can be readily found. For cases when the height is not available, Hero's Formula can be used: www.automathic.org/2_heros-formula



By AFM

Tags: Pyramid, volume,

0

Posted: 2013-04-10
Volume of a pyramid
Volume of a pyramid
$$$V = b/3*h $$$

b = surface area of the base of the pyramid

I've spent a long time working this out from more basic principles on several occasions. Proving it seems simple but it ain't.



By AFM

Tags: trig, trigonometry

0

Posted: 2013-04-10
Trigonometric Functions
Trigonometric Functions
$$$Sine = opposite/hypotenuse \\ Cosine = adjacent/hypotenuse \\ Tangent = opposite/adjacent$$$

These three most common trig functions can be recalled with the mnemonic Soh Cah Toa

There are also three more trig functions:

Secant Cosecant Cotangent

In order to properly explain these six chessnuts, we'll need to add a diagram, which Automathic doesn't yet permit.



By PiThagoras

Tags: Long Division, Division, Quotient, Remainder, Divisor,...

0

Posted: 2013-04-09
Long Division Procedure
Long Division Procedure

1. When dividing two numbers, for example, n divided by m, n is the dividend and m is the divisor; the answer is the quotient.
2. Find the location of all decimal points in the dividend and divisor.
3. If necessary, simplify the long division problem by moving the decimals of the divisor and dividend by the same number of decimal places, to the right, (or to the left) so that the decimal of the divisor is to the right of the last digit.
4. When doing long division, keep the numbers lined up straight from top to bottom under the tableau.
5. After each step, be sure the remainder for that step is less than the divisor. If it is not, there are three possible problems: the multiplication is wrong, the subtraction is wrong, or a greater quotient is needed.
6. In the end, the remainder, r, is added to the growing quotient as a fraction, \(r/m\)

More info can be found on Wikipedia: http://en.wikipedia.org/wiki/Long_division



By WattsNephew

Tags: work, mass, acceleration, distance

0

Posted: 2013-04-28
Work Calculation
Work Calculation
$$$W = m*a*d$$$

Work makes you mad. Simple - at least according to my high school chemistry teacher.

Actually, not so simple. Work is the product of a force (mass multiplied by acceleration) and a distance; in other words, a force does work when it moves an object some distance. So, when you lift a rock above your head, you have done work. Obviously.

The units are odd too. In the SI system, work is measured in Joules (Newton-Meters). To us Americans working on cars, it is measured in foot-pounds (feet for the distance and pounds for the force). Funny, eh?

You can read more at http://en.wikipedia.org/wiki/Work_%28physics%29.



By Per

Tags: Relation, Heisenberg

0

Posted: 2013-07-07
Uncertainty relation
Uncertainty relation
$$$\Delta p \Delta x \geq {h \over 4 \pi}$$$

This relation is called Heisenbergs uncertainty relation and tells us how a precise measurement in position ($$x$$) yields a spread in the momentum ($$p$$) or vice versa. Here $$h$$ is a very small quantity $$\sim 10^{-34}Js$$ and is called Planck's constant.



By PiThagoras

Tags: Circle, Circumference, Radius, Diameter, Pi, Area

0

Posted: 2013-08-26
Radius of a Circle
Radius of a Circle
$$$D = {C \over pi} \; \; \; or \; \; \; R = {C \over 2 \pi}$$$

If you need to determine the Radius ($$R$$) or Diameter ($$D$$) of a circle and only have the Circumference ($$C$$), you can do that with this formula.



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