Formulas in physics 6 8. Basic formulas in physics - mechanics

Mechanics
1. Pressure P=F/S
2. Density ρ=m/V
3. Pressure at the depth of the liquid P=ρ∙g∙h
4. Gravity Ft=mg
5. Archimedean force Fa=ρzh∙g∙Vt
6. Equation of motion for uniformly accelerated motion
m(g+a)
m(ga)
X=X0+υ0∙t+(a∙t2)/2 S= (υ2υ0
2) /2a S= (υ+υ0) ∙t /2
7. Velocity equation for uniformly accelerated motion υ=υ0+a∙t
8. Acceleration a=(υυ 0)/t
9. Speed ​​when moving in a circle υ=2πR/T
10. Centripetal acceleration a=υ2/R
11. Relationship between period and frequency ν=1/T=ω/2π
12.
Newton's II law F=ma
13. Hooke's law Fy=kx
14. Law of Universal Gravitation F=G∙M∙m/R2
15. Weight of a body moving with acceleration a P =
16. Weight of a body moving with acceleration a P =
17. Friction force Ftr=µN
18. Body momentum p=mυ
19. Force impulse Ft=∆p
20. Moment of force M=F∙?
21. Potential energy of a body raised above the ground Ep=mgh
22. Potential energy of an elastically deformed body Ep=kx2/2
23. Kinetic energy of the body Ek=mυ2/2
24. Work A=F∙S∙cosα
25. Power N=A/t=F∙υ
26. Efficiency η=Ap/Az
27. Period of oscillation of a mathematical pendulum T=2 √?/π
28. Period of oscillation of a spring pendulum T=2
29. Equation of harmonic vibrations Х=Хmax∙cos
30. Relationship between wavelength, its speed and period λ= υТ

Molecular Physics and
thermodynamics
31. Amount of substance ν=N/ Na
32. Molar mass
33. Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
34. Basic equation of MKT P=nkT=1/3nm0υ2
35. Gay – Lussac’s law (isobaric process) V/T =const
36. Charles’s law (isochoric process) P/T =const
37. Relative humidity φ=P/P0∙100%
38. Int. energy ideal. monatomic gas U=3/2∙M/µ∙RT
39. Gas work A=P∙ΔV
40. Boyle’s law – Mariotte (isothermal process) PV=const
41. Amount of heat during heating Q=Cm(T2T1)
g
√π m/k
tω

↓
M=m/ν
Optics
86. Law of light refraction n21=n2/n1= υ 1/ υ 2
87. Refractive index n21=sin α/sin γ
88. Thin lens formula 1/F=1/d + 1/f
89. Lens optical power D=1/F
90.max interference: Δd=kλ,
91. min interference: Δd=(2k+1)λ/2
92. Differential grating d∙sin φ=k λ
The quantum physics
93. Fla Einstein for photo effect
hν=Aout+Ek, Ek=Uze
94. Red border of the photoelectric effect νк = Aout/h
95. Photon momentum P=mc=h/ λ=E/s
Physics of the atomic nucleus
96. Law of radioactive decay N=N0∙2t/T
97. Binding energy of atomic nuclei
ECB=(Zmp+NmnМя)∙c2
ONE HUNDRED
t=t1/√1υ2/c2
98.
99. ?=?0∙√1υ2/c2
100. υ2=(υ1+υ)/1+ υ1∙υ/c2
101. E = mc2
42. Amount of heat during melting Q= mλ
43. Amount of heat during vaporization Q=Lm
44. Amount of heat during fuel combustion Q=qm
45. Equation of state of an ideal gas
PV=m/M∙RT
46. ​​First law of thermodynamics ΔU=A+Q
47. Efficiency of heat engines = (η Q1 Q2)/ Q1
48. Efficiency ideal. engines (Carnot cycle) = (Тη
1 T2)/ T1
Electrostatics and electrodynamics
49. Coulomb's law F=k∙q1∙q2/R2
50. Electric field strength E=F/q
51. Electrical tension point charge field E=k∙q/R2
52. Surface charge density σ = q/S
53. Electrical tension fields of an infinite plane E=2 kπ σ
54. Dielectric constant ε=E0/E
55. Potential energy of interaction. charges W= k∙q1q2/R
56. Potential φ=W/q
57. Point charge potential =φ k∙q/R
58. Voltage U=A/q
59. For a uniform electric field U=E∙d
60. Electric capacity C=q/U
61. Electric capacity of a flat capacitor C=S∙ε∙ε0/d
62. Energy of a charged capacitor W=qU/2=q²/2С=CU²/2
63. Current strength I=q/t
64. Conductor resistance R=ρ∙?/S
65. Ohm's law for the circuit section I=U/R
66. Laws of the last. connections I1=I2=I, U1+U2=U, R1+R2=R
67. Laws parallel. conn. U1=U2=U, I1+I2=I, 1/R1+1/R2=1/R
68. Electric current power P=I∙U
69. Joule-Lenz's law Q=I2Rt
70. Ohm's law for a complete chain I=ε/(R+r)
71. Short circuit current (R=0) I=ε/r
72. Magnetic induction vector B=Fmax/?∙I
73. Ampere force Fa=IB?sin α
74. Lorentz force Fl=Bqυsin α
75. Magnetic flux Ф=BSсos α Ф=LI
76. Law of electromagnetic induction Ei=ΔФ/Δt
77. Induction emf in a moving conductor Ei=B?υsinα
78. Self-induction EMF Esi=L∙ΔI/Δt
79. Magnetic field energy of the coil Wm=LI2/2
80. Oscillation period no. circuit T=2 ∙√π LC
81. Inductive reactance XL= Lω =2 Lπ ν
82. Capacitance Xc=1/ Cω
83. Effective current value Id=Imax/√2,
84. Effective voltage value Ud=Umax/√2
85. Impedance Z=√(XcXL)2+R2

The session is approaching, and it’s time for us to move from theory to practice. Over the weekend we sat down and thought that many students would benefit from having a collection of basic physics formulas at their fingertips. Dry formulas with explanation: short, concise, nothing superfluous. A very useful thing when solving problems, you know. And during an exam, when exactly what was memorized the day before might “jump out of your head,” such a selection will serve an excellent purpose.

The most problems are usually asked in the three most popular sections of physics. This Mechanics, thermodynamics And Molecular physics, electricity. Let's take them!

Basic formulas in physics dynamics, kinematics, statics

Let's start with the simplest. The good old favorite straight and uniform movement.

Kinematics formulas:

Of course, let's not forget about motion in a circle, and then we'll move on to dynamics and Newton's laws.

After dynamics, it’s time to consider the conditions of equilibrium of bodies and liquids, i.e. statics and hydrostatics

Now we present the basic formulas on the topic “Work and Energy”. Where would we be without them?

Basic formulas of molecular physics and thermodynamics

Let's finish the mechanics section with formulas for oscillations and waves and move on to molecular physics and thermodynamics.

The efficiency factor, the Gay-Lussac law, the Clapeyron-Mendeleev equation - all these formulas dear to the heart are collected below.

By the way! There is now a discount for all our readers 10% on .

Basic formulas in physics: electricity

It's time to move on to electricity, even though it is less popular than thermodynamics. Let's start with electrostatics.

And, to the beat of the drum, we end with formulas for Ohm’s law, electromagnetic induction and electromagnetic oscillations.

That's all. Of course, a whole mountain of formulas could be cited, but this is of no use. When there are too many formulas, you can easily get confused and even melt your brain. We hope our cheat sheet of basic physics formulas will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or haven’t found the right formula: ask the experts student service. Our authors keep hundreds of formulas in their heads and crack problems like nuts. Contact us, and soon any task will be up to you.

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1 BASIC FORMULAS IN PHYSICS FOR STUDENTS OF TECHNICAL UNIVERSITIES.. Physical foundations of mechanics. Instantaneous velocity dr r- radius vector of the material point, t- time, Module of instantaneous velocity s- distance along the trajectory of motion, Path length Acceleration: instantaneous tangential normal total τ- unit vector tangent to the trajectory; R is the radius of curvature of the trajectory, n is the unit vector of the main normal. ANGULAR SPEED ds = S t t t d a d a a n n R a a a, n a a a n d φ - angular displacement. Angular acceleration d.. Relationship between linear and.. angular quantities s= φr, υ= ωr, and τ = εr, and n = ω R.3. Impulse.4. material point p mass of the material point. Basic equation of the dynamics of a material point (Newton's second law)

2 a dp Fi, Fi Law of conservation of momentum for an isolated mechanical system Radius vector of the center of mass Dry friction force μ - friction coefficient, N - normal pressure force. Elastic force k- coefficient of elasticity (stiffness), Δl- deformation..4.. Force of gravitational r F i i onst r i N F in =k Δl, i i.4.. interactions.4.3. F G r and are the particle masses, G is the gravitational constant, r is the distance between particles. Work of force A FdS da Power N F Potential energy: k(l) of an elastically deformed body P = gravitational interaction of two particles P = G r body in a uniform gravitational field g - gravitational field strength (gravitational acceleration), h - distance from the zero level. P=gh

3.4.4. Gravitational tension.4.5. Earth's field g= G (R h) 3 is the mass of the Earth, R 3 is the radius of the Earth, h is the distance from the surface of the Earth. Potential of the Earth's gravitational field 3 Kinetic energy of a material point φ= G T= (R 3 3 h) p Law of conservation of mechanical energy for a mechanical system E=T+P=onst Moment of inertia of a material point J=r r- distance to the axis of rotation. Moments of inertia of bodies with mass relative to an axis passing through the center of mass: a thin-walled cylinder (ring) of radius R, if the axis of rotation coincides with the axis of the cylinder J o = R solid cylinder (disk) of radius R, if the axis of rotation coincides with the axis of the cylinder J o = R a ball of radius R J о = 5 R a thin rod of length l, if the axis of rotation is perpendicular to the rod J о = l Moment of inertia of a body with mass relative to an arbitrary axis (Steiner’s theorem) J=J +d

4 J is the moment of inertia about a parallel axis passing through the center of mass, d is the distance between the axes. The moment of force acting on a material point relative to the origin of coordinates r is the radius vector of the point of application of the force. Momentum of the system.4.8. relative to the Z axis r F N.4.9. L z J iz iz i.4.. Basic equation of dynamics.4.. of rotational motion Law of conservation of angular momentum for an isolated system Work during rotational motion dl, J.4.. Σ J i ω i =onst A d Kinetic energy of a rotating body J T= L J Relativistic length contraction l l lо the length of a body at rest c is the speed of light in vacuum. Relativistic time dilation t t t o proper time. Relativistic mass o rest mass Rest energy of the particle E o = o c

5.4.3. Total relativistic energy.4.4. particles.4.5. E=.4.6. Relativistic impulse P=.4.7. Kinetic energy.4.8. relativistic particle.4.9. T = E- E o = Relativistic relationship between total energy and momentum E = p c + E o The law of addition of velocities in relativistic mechanics and and and - velocities in two inertial reference systems moving relative to each other with a speed υ coinciding in direction with and (sign -) or oppositely directed (sign +) u u u Physics of mechanical vibrations and waves. The displacement of the oscillating material point s Aos(t) A is the amplitude of the oscillation, is the natural cyclic frequency, φ o is the initial phase. Cyclic frequency T

6 T period of oscillation - frequency Speed ​​of an oscillating material point Acceleration of an oscillating material point Kinetic energy of a material point performing harmonic oscillations v ds d s a v T Potential energy of a material point performing harmonic oscillations Ï kx stiffness coefficient (elasticity coefficient) Total energy of a material point performing harmonic oscillations oscillations A sin(t) dv E T Ï A os(t) A A A sin (t) os (t) d s Differential equation s of free harmonic undamped oscillations of quantity s d s ds Differential equation s of free damped oscillations of quantity s, - damping coefficient A(t) T Logarithmic decrement ln T A(T t) of damping, relaxation time d s ds Differential equation s F ost Period of oscillation of pendulums: spring T, k

7 physical T J, gl - mass of the pendulum, k - spring stiffness, J - moment of inertia of the pendulum, g - gravitational acceleration, l - distance from the suspension point to the center of mass. Equation of a plane wave propagating in the direction of the Ox axis, v speed of wave propagation Wave length T - wave period, v - speed of wave propagation, oscillation frequency Wave number Speed ​​of sound propagation in gases γ - ratio of the heat capacities of gas, at constant pressure and volume, R- molar gas constant, T- thermodynamic temperature, M- molar mass of gas x (x, t) Aos[ (t) ] v v T v vt v RT Molecular physics and thermodynamics..4.. Amount of substance N N A, N- number of molecules, N A - Avogadro's constant - mass of substance M molar mass. Clapeyron-Mendeleev equation p = ν RT,

8 p is the gas pressure, is its volume, R is the molar gas constant, T is the thermodynamic temperature. Equation of molecular kinetic theory of gases Р= 3 n<εпост >= 3 no<υ кв >n is the concentration of molecules,<ε пост >- average kinetic energy of translational motion of a molecule. o - molecular mass<υ кв >- root mean square speed. Average molecular energy<ε>= i kt i - number of degrees of freedom k - Boltzmann constant. Internal energy of an ideal gas U= i νrt Molecular velocities: root mean square<υ кв >= 3kT = 3RT ; arithmetic mean<υ>= 8 8RT = kt ; most likely<υ в >= Average free length kt = RT ; path of a molecule d-effective diameter of a molecule Average number of collisions (d n) of a molecule per unit time z d n v

9 Distribution of molecules in a potential force field P is the potential energy of a molecule. Barometric formula p - gas pressure at height h, p - gas pressure at a level taken as zero, - molecular mass, Fick's Diffusion Law j - mass flow density, n n exp kt gh p p exp kt j d ds d =-D dx d - density gradient, dx D - diffusion coefficient, ρ - density, d - gas mass, ds - elementary area perpendicular to the Ox axis. Fourier's law of thermal conductivity j - heat flux density, Q j Q dq ds dt =-æ dx dt - temperature gradient, dx æ - thermal conductivity coefficient, Internal friction force η - dynamic viscosity coefficient, dv df ds dz d - velocity gradient, dz Coefficient diffusion D= 3<υ><λ>Coefficient of dynamic viscosity (internal friction) v 3 D Thermal conductivity coefficient æ = 3 сv ρ<υ><λ>=ηс v

10 s v specific isochoric heat capacity, Molar heat capacity of an ideal gas isochoric isobaric First law of thermodynamics i C v R i C p R dq=du+da, da=pd, du=ν C v dt Work of gas expansion during an isobaric process A=p( -)= ν R(T -T) isothermal p А= ν RT ln = ν RT ln p adiabatic A C T T) γ=с р/С v (RT A () p A= () Poisson's equations Carnot cycle efficiency. 4.. Q n and T n - the amount of heat received from the heater and its temperature; Q x and T x - the amount of heat transferred to the refrigerator and its temperature. The change in entropy during the transition of the system from state to state P γ =onst T γ- =onst T γ r - γ =onst Qí Q Q S S í õ Tí T T dq T í õ

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Cheat sheet with formulas in physics for the Unified State Exam

and more (may be needed for grades 7, 8, 9, 10 and 11).

First, a picture that can be printed in a compact form.

Mechanics

1. Pressure P=F/S
2. Density ρ=m/V
3. Pressure at liquid depth P=ρ∙g∙h
4. Gravity Ft=mg
5. 5. Archimedean force Fa=ρ f ∙g∙Vt
6. Equation of motion for uniformly accelerated motion

X=X 0 + υ 0 ∙t+(a∙t 2)/2 S=( υ 2 -υ 0 2) /2a S=( υ +υ 0) ∙t /2

1. Velocity equation for uniformly accelerated motion υ =υ 0 +a∙t
2. Acceleration a=( υ -υ 0)/t
3. Circular speed υ =2πR/T
4. Centripetal acceleration a= υ 2/R
5. Relationship between period and frequency ν=1/T=ω/2π
6. Newton's II law F=ma
7. Hooke's law Fy=-kx
8. Law of Gravity F=G∙M∙m/R 2
9. Weight of a body moving with acceleration a P=m(g+a)
10. Weight of a body moving with acceleration а↓ Р=m(g-a)
11. Friction force Ftr=µN
12. Body momentum p=m υ
13. Force impulse Ft=∆p
14. Moment of force M=F∙ℓ
15. Potential energy of a body raised above the ground Ep=mgh
16. Potential energy of an elastically deformed body Ep=kx 2 /2
17. Kinetic energy of the body Ek=m υ 2 /2
18. Work A=F∙S∙cosα
19. Power N=A/t=F∙ υ
20. Efficiency η=Ap/Az
21. Oscillation period of a mathematical pendulum T=2π√ℓ/g
22. Oscillation period of a spring pendulum T=2 π √m/k
23. Equation of harmonic vibrations Х=Хmax∙cos ωt
24. Relationship between wavelength, its speed and period λ= υ T

Molecular physics and thermodynamics

1. Amount of substance ν=N/Na
2. Molar mass M=m/ν
3. Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
4. Basic MKT equation P=nkT=1/3nm 0 υ 2
5. Gay-Lussac's law (isobaric process) V/T =const
6. Charles's law (isochoric process) P/T =const
7. Relative humidity φ=P/P 0 ∙100%
8. Int. energy ideal. monatomic gas U=3/2∙M/µ∙RT
9. Gas work A=P∙ΔV
10. Boyle–Mariotte law (isothermal process) PV=const
11. Amount of heat during heating Q=Cm(T 2 -T 1)
12. Amount of heat during melting Q=λm
13. Amount of heat during vaporization Q=Lm
14. Amount of heat during fuel combustion Q=qm
15. Equation of state of an ideal gas PV=m/M∙RT
16. First law of thermodynamics ΔU=A+Q
17. Efficiency of heat engines η= (Q 1 - Q 2)/ Q 1
18. Efficiency is ideal. engines (Carnot cycle) η= (T 1 - T 2)/ T 1

Electrostatics and electrodynamics - formulas in physics

1. Coulomb's law F=k∙q 1 ∙q 2 /R 2
2. Electric field strength E=F/q
3. Electrical tension point charge field E=k∙q/R 2
4. Surface charge density σ = q/S
5. Electrical tension fields of an infinite plane E=2πkσ
6. Dielectric constant ε=E 0 /E
7. Potential energy of interaction. charges W= k∙q 1 q 2 /R
8. Potential φ=W/q
9. Point charge potential φ=k∙q/R
10. Voltage U=A/q
11. For a uniform electric field U=E∙d
12. Electric capacity C=q/U
13. Electric capacity of a flat capacitor C=S∙ ε ∙ε 0 /d
14. Energy of a charged capacitor W=qU/2=q²/2С=CU²/2
15. Current strength I=q/t
16. Conductor resistance R=ρ∙ℓ/S
17. Ohm's law for the circuit section I=U/R
18. Laws of the last. connections I 1 =I 2 =I, U 1 +U 2 =U, R 1 +R 2 =R
19. Laws parallel. conn. U 1 =U 2 =U, I 1 +I 2 =I, 1/R 1 +1/R 2 =1/R
20. Electric current power P=I∙U
21. Joule-Lenz law Q=I 2 Rt
22. Ohm's law for a complete circuit I=ε/(R+r)
23. Short circuit current (R=0) I=ε/r
24. Magnetic induction vector B=Fmax/ℓ∙I
25. Ampere power Fa=IBℓsin α
26. Lorentz force Fl=Bqυsin α
27. Magnetic flux Ф=BSсos α Ф=LI
28. Law of electromagnetic induction Ei=ΔФ/Δt
29. Induction emf in a moving conductor Ei=Вℓ υ sinα
30. Self-induction EMF Esi=-L∙ΔI/Δt
31. Coil magnetic field energy Wm=LI 2 /2
32. Oscillation period no. circuit T=2π ∙√LC
33. Inductive reactance X L =ωL=2πLν
34. Capacitance Xc=1/ωC
35. Effective current value Id=Imax/√2,
36. Effective voltage value Uд=Umax/√2
37. Impedance Z=√(Xc-X L) 2 +R 2

Optics

1. Law of light refraction n 21 =n 2 /n 1 = υ 1 / υ 2
2. Refractive index n 21 =sin α/sin γ
3. Thin lens formula 1/F=1/d + 1/f
4. Lens optical power D=1/F
5. max interference: Δd=kλ,
6. min interference: Δd=(2k+1)λ/2
7. Differential grid d∙sin φ=k λ

The quantum physics

1. Einstein's formula for the photoelectric effect hν=Aout+Ek, Ek=U z e
2. Red border of the photoelectric effect ν k = Aout/h
3. Photon momentum P=mc=h/ λ=E/s

Physics of the atomic nucleus

1. Law of radioactive decay N=N 0 ∙2 - t / T
2. Binding energy of atomic nuclei

Good afternoon, dear radio amateurs!
Welcome to the website ““

The formulas form the skeleton of the science of electronics. Instead of dumping a whole bunch of radio elements on the table and then reconnecting them together, trying to figure out what will be born as a result, experienced specialists immediately build new circuits based on known mathematical and physical laws. It is the formulas that help determine the specific values ​​of the ratings of electronic components and operating parameters of circuits.

It is just as effective to use formulas to modernize ready-made circuits. For example, in order to select the correct resistor in a circuit with a light bulb, you can apply the basic Ohm’s law for direct current (you can read about it in the section “Relationships of Ohm’s Law” immediately after our lyrical introduction). The light bulb can thus be made to shine more brightly or, conversely, dimmed.

This chapter will present many basic physics formulas that sooner or later you will encounter while working in electronics. Some of them have been known for centuries, but we still continue to use them successfully, as will our grandchildren.

Ohm's law relations

Ohm's Law is the relationship between voltage, current, resistance and power. All derived formulas for calculating each of these values ​​are presented in the table:

This table uses the following generally accepted designations for physical quantities:

U- voltage (V),

I- current (A),

R- Power, W),

R- resistance (Ohm),

Let's practice using the following example: let's say we need to find the power of the circuit. It is known that the voltage at its terminals is 100 V and the current is 10 A. Then the power according to Ohm’s law will be equal to 100 x 10 = 1000 W. The obtained value can be used to calculate, say, the fuse rating that needs to be entered into the device, or, for example, to estimate the electricity bill that an electrician from the housing office will personally bring to you at the end of the month.

Here's another example: let's say we need to find out the value of the resistor in a circuit with a light bulb, if we know what current we want to pass through this circuit. According to Ohm's law, the current is equal to:

I=U/R

A circuit consisting of a light bulb, a resistor and a power source (battery) is shown in the figure. Using the above formula, even a schoolchild can calculate the required resistance.

What is what in this formula? Let's take a closer look at the variables.

> U pit(sometimes also written as V or E): supply voltage. Due to the fact that when current passes through the light bulb, some voltage drops across it, the magnitude of this drop (usually the operating voltage of the light bulb, in our case 3.5 V) must be subtracted from the voltage of the power source. For example, if Upit = 12 V, then U = 8.5 V, provided that 3.5 V drops across the light bulb.

> I: The current (measured in amperes) that is planned to flow through the light bulb. In our case - 50 mA. Since the current in the formula is indicated in amperes, 50 milliamps is only a small part of it: 0.050 A.

> R: the desired resistance of the current-limiting resistor, in ohms.

In continuation, you can put real numbers in the formula for calculating resistance instead of U, I and R:

R = U/I = 8.5 V / 0.050 A = 170 Ohm

Resistance calculations

Calculating the resistance of one resistor in a simple circuit is quite simple. However, as other resistors are added to it, either in parallel or in series, the overall resistance of the circuit also changes. The total resistance of several resistors connected in series is equal to the sum of the individual resistances of each of them. For a parallel connection, everything is a little more complicated.

Why do you need to pay attention to the way components are connected to each other? There are several reasons for this.

> Resistor resistances are only a certain fixed range of values. In some circuits, the resistance value must be calculated accurately, but since a resistor of exactly this value may not exist at all, several elements must be connected in series or in parallel.

> Resistors are not the only components that have resistance. For example, the turns of an electric motor winding also have some resistance to current. In many practical problems, it is necessary to calculate the total resistance of the entire circuit.

Calculation of the resistance of series resistors

The formula for calculating the total resistance of resistors connected in series is indecently simple. You just need to add up all the resistances:

Rtotal = Rl + R2 + R3 + … (as many times as there are elements)

In this case, the values ​​Rl, R2, R3 and so on are the resistances of individual resistors or other circuit components, and Rtotal is the resulting value.

So, for example, if there is a circuit of two resistors connected in series with values ​​of 1.2 and 2.2 kOhm, then the total resistance of this section of the circuit will be equal to 3.4 kOhm.

Calculation of the resistance of parallel resistors

Things get a little more complicated if you need to calculate the resistance of a circuit consisting of parallel resistors. The formula takes the form:

R total = R1 * R2 / (R1 + R2)

where R1 and R2 are the resistances of individual resistors or other circuit elements, and Rtot is the resulting value. So, if we take the same resistors with values ​​of 1.2 and 2.2 kOhm, but connected in parallel, we get

776,47 = 2640000 / 3400

To calculate the resulting resistance of an electrical circuit of three or more resistors, use the following formula:

Capacity calculations

The formulas given above are also valid for calculating capacities, only exactly the opposite. Just like resistors, they can be extended to cover any number of components in a circuit.

Calculation of the capacitance of parallel capacitors

If you need to calculate the capacitance of a circuit consisting of parallel capacitors, you simply need to add their values:

Commun = CI + C2 + SZ + ...

In this formula, CI, C2 and SZ are the capacitances of individual capacitors, and Ctotal is a summing value.

Calculation of the capacitance of series capacitors

To calculate the total capacitance of a pair of capacitors connected in series, the following formula is used:

Commun = C1 * C2 / (C1 + C2)

where C1 and C2 are the capacitance values ​​of each capacitor, and Ctot is the total capacitance of the circuit

Calculation of the capacitance of three or more series-connected capacitors

Are there capacitors in the circuit? A lot of? It's okay: even if they are all connected in series, you can always find the resulting capacitance of this circuit:

So why connect several capacitors in series at once when one could suffice? One of the logical explanations for this fact is the need to obtain a specific value for the circuit capacitance, which has no analogue in the standard series of ratings. Sometimes you have to go down a more thorny path, especially in sensitive circuits such as radio receivers.

Calculation of energy equations

The most widely used unit of energy measurement in practice is kilowatt-hours or, in the case of electronics, watt-hours. You can calculate the energy expended by the circuit by knowing the length of time during which the device is turned on. The formula for calculation is:

watt hours = P x T

In this formula, the letter P denotes power consumption, expressed in watts, and T is the operating time in hours. In physics, it is customary to express the amount of energy expended in watt-seconds, or Joules. To calculate energy in these units, watt-hours are divided by 3600.

Calculation of constant capacitance of an RC circuit

Electronic circuits often use RC circuits to provide time delays or lengthen pulse signals. The simplest circuits consist of just a resistor and a capacitor (hence the origin of the term RC circuit).

The operating principle of an RC circuit is that a charged capacitor is discharged through a resistor not instantly, but over a certain period of time. The greater the resistance of the resistor and/or capacitor, the longer the capacitance will take to discharge. Circuit designers very often use RC circuits to create simple timers and oscillators or alter waveforms.

How can you calculate the time constant of an RC circuit? Since this circuit consists of a resistor and a capacitor, the resistance and capacitance values ​​are used in the equation. Typical capacitors have a capacitance on the order of microfarads or even less, and the system units are farads, so the formula operates in fractional numbers.

T=RC

In this equation, T stands for time in seconds, R stands for resistance in ohms, and C stands for capacitance in farads.

Let, for example, have a 2000 ohm resistor connected to a 0.1 µF capacitor. The time constant of this chain will be equal to 0.002 s, or 2 ms.

In order to make it easier for you at first to convert ultra-small units of capacitance into farads, we have compiled a table:

Frequency and wavelength calculations

The frequency of a signal is a quantity inversely proportional to its wavelength, as will be seen from the formulas below. These formulas are especially useful when working with radio electronics, for example, for estimating the length of a piece of wire that is planned to be used as an antenna. In all the following formulas, wavelength is expressed in meters and frequency in kilohertz.

Signal frequency calculation

Suppose you want to study electronics in order to build your own transceiver and chat with similar enthusiasts from another part of the world on an amateur radio network. The frequencies of radio waves and their length stand side by side in the formulas. In amateur radio networks you can often hear statements that the operator works on such and such a wavelength. Here's how to calculate the frequency of a radio signal given the wavelength:

Frequency = 300000 / wavelength

The wavelength in this formula is expressed in millimeters, and not in feet, arshins or parrots. The frequency is given in megahertz.

Signal wavelength calculation

The same formula can be used to calculate the wavelength of a radio signal if its frequency is known:

Wavelength = 300000 / Frequency

The result will be expressed in millimeters, and the signal frequency is indicated in megahertz.

Let's give an example of a calculation. Let a radio amateur communicate with his friend on a frequency of 50 MHz (50 million cycles per second). Substituting these numbers into the above formula, we get:

6000 millimeters = 300000/ 50 MHz

However, more often they use system units of length - meters, so to complete the calculation we just need to convert the wavelength into a more understandable value. Since there are 1000 millimeters in 1 meter, the result is 6 m. It turns out that the radio amateur tuned his radio station to a wavelength of 6 meters. Cool!