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1

Equivalent capacitance for capacitors in series

Ceq =1/( 1/C₁ + 1/C₂ + ... + 1/Cₙ)

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2

Equivalent capacitance for capacitors in parallel

C_eq = C₁ + C₂ + ... + Cₙ

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3

Magnification of an image (two equations)

m = -di/do = hi/ho

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4

mass-energy equivalence

E=mc²

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5

momentum of a photon

p = h/λ, E/c, hf/c

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6

work function if cutoff wavelength is known

Φ=hc/λ

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7

Photoelectric effect including stopping potential

Ephoton=qVs+Φ

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8

Photoelectric Effect including Kmax

Kmax=Ephoton-Φ

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9

energy of a photon

E = hf, hc/λ

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10

EMF generated for a moving bar through a Magnetic field

EMF = Blv

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11

Faraday’s law of electromagnetic induction

E=-∆Φ/∆t=(-∆NBA/∆t)

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12

magnetic flux

Φ=NBA=NBAcosθ

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13

thin lens equation

1/f = 1/do + 1/di

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14

snell's law

n₁sinθ₁ = n₂sinθ₂

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15

index of refraction

n = c/v

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16

critical angle

sinθ=n₂/n₁

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17

Thin film(membrane interference

2nt=__λ

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18

total resistance for resistors in series

Rt= R₁ + R₂ + R₃ + ... + Rₙ

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19

total resistance for resistors in parallel

Rt= (R₁⁻¹ + R₂⁻¹ + R₃⁻¹ + ... + Rₙ⁻¹)⁻¹

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20

Charge including time

Q=It

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21

Resistance in a wire of length L and area A

R=ρ(L/A)

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22

Pressure exerted on an area A

P = F/A

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23

absolute pressure

Pabs=P₀+ρgh

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24

gauge pressure

ρgh

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25

Volume flow rate

I=AV

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26

Buoyant force

F=ρVg

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27

Density

ρ=m/v

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28

bernoulli's equation

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

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29

Force on a charge q moving parallel to a magnetic field (B)

0 N

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30

Force on a current carrying wire oriented perpendicular to a magnetic field (B)

F=Il×B

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31

capacitance if area of plates is known

C = KεA/d

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32

Electric Potential around a point charge q

V = kq/r

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33

Force on a charge (q) in an Electric field (E)

F = qE

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34

coulomb's law

F = kq₁q₂/r², where k=1/(4πε₀)

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35

charge on a capacitor

Q=CV

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36

Energy stored in a capacitor (3 formulas)

Ucap=½QV=½CV²=½Q²/C

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37

Formula definition of Work

W=F∙d

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38

electric potential energy

Ue= qV

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39

Electric field a distance r from a point charge (q)

F = k|q|/r²

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40

Ohm’s Law

V=IR

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41

Total charge for capacitors in series

Qt=Q₁=Q₂=Q₃

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42

Terminal voltage (Vab) if external resistance (Rext) is known

Vab=I₁Rext

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43

Terminal voltage (Vab) if EMF is known

ε=Vab-I₁R(int)

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44

Voltage across the plates of a capacitor if the E-field is known

Ed=V

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45

Electric Energy (three formulas)

E=VIt=V²Rt=I²Rt

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46

Electric Power

P=VI=V²R=I²R

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47

Force on a charge (q) moving perpendicularly through a magnetic field (B)

F=qv×B

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48

Work to move a point charge (q) a distance r away from another charge (Q)

w=q∆V

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49

Force between two parallel current carrying wires of length l.

F=(µ₀/2π)(I₁I₂l/r) (the third one is L)

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50

Limits of human sight

750 nm-400nm

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51

the wave equation

v=fλ

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52

Magnetic field a distance r from a current carrying wire

B=(µ₀/2π)(I/r)

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53

New wavelength in the original wavelength and the indices of refraction are known

n₁λ₁=n₂λ₂

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54

Change in Heat during an isovolumetric process

Q = nCvΔT

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55

Frequency of a spring mass

f = 1/(2π) * √(k/m)

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56

period of a pendulum

T = 2π√(L/g)

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57

frictional force

F=Fₙµ

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58

frictional force on an incline

mg(cosθ)µ

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59

Acceleration

a= ∆v/∆t

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60

average speed

s = d/t

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61

velocity

v= ∆x/∆t

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62

Average Velocity of a molecule of gas

v = √(3kT/m)

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63

Change in internal energy during a cyclic process

ΔU = 0 J

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64

First Law of thermodynamics

ΔU = ∆Q + ∆W

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65

Acceleration of a mass sliding UP an incline, with friction

a = gsinθ + gμcosθ

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66

Acceleration of a mass sliding DOWN an incline, with friction

a = gsinθ - gμcosθ

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67

Heat required to raise the temperature of a substance

Q = mcΔT

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68

Heat required to vaporize a substance

Q = mLv

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69

Heat required to melt a substance

Q = m(Lf)

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70

Forgotten power equation

P=Fv

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71

Energy of a spring-mass when spring is neither at maximum displacement, nor at the equilibrium point

½kA²=½mv²+½kx²

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72

ideal efficiency

ε=(T_hot - T_cold) / T_hot x100

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73

Newton's second law of motion

F = ma

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74

torque

∑τ=r×F=rFsinθ

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75

Ideal gas law (two equations)

PV = nRT or PV=NKT

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76

Boyle's law

P₁V₁ = P₂V₂

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77

heat of an isobaric process

Q = nCpΔT

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78

work (thermodynamics)

W = -PΔV

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79

internal energy of an ideal gas

U = (3/2) nRT

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80

actual efficiency

εactual=|∑W|/Qin=|Qin-Qout|/Qin

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81

kinetic energy

KE = ½mv²

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82

Hooke's Law

F = -kx

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83

gravitational potential energy

Ug = mgh or mg∆y

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84

Newton's Law of Universal Gravitation'

F = G (m₁ m₂) / r²

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85

centripetal acceleration

a = v²/r

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86

Acceleration due to gravity at the surface of a planet of mass M and diameter d

g = (G*M) / (d/2)²

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87

momentum

p = mv

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88

impulse (two formulas)

J = Ft or J = mv-mv₀

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89

weight

W or Fg=mg

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90

first kinematic

v = v₀ + at

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91

second kinematic

∆x = v₀t + ½at²

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92

third kinematic

v²=v₀²+2a∆x

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93

beat frequency

f = |f1 - f2|

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94

Length (L) of a string producing the fundamental frequency (f)

L=v/2f

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95

Natural frequency of a closed tube of length l

L=v/4f

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96

Wavelength in an open tube of length l

λ=2L

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97

frequency of a pendulum

f = 1/T = 1/(2π √(l/g))

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98

Velocity of waves on a string if tension is known

v = √(T/(m/l))

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99

period of a spring-mass

T = 2π√(m/k)

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100

charles' law

V₁/T₁ = V₂/T₂

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