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Equivalent capacitance for capacitors in series
Ceq =1/( 1/C₁ + 1/C₂ + ... + 1/Cₙ)
Equivalent capacitance for capacitors in parallel
C_eq = C₁ + C₂ + ... + Cₙ
Magnification of an image (two equations)
m = -di/do = hi/ho
mass-energy equivalence
E=mc²
momentum of a photon
p = h/λ, E/c, hf/c
work function if cutoff wavelength is known
Φ=hc/λ
Photoelectric effect including stopping potential
Ephoton=qVs+Φ
Photoelectric Effect including Kmax
Kmax=Ephoton-Φ
energy of a photon
E = hf, hc/λ
EMF generated for a moving bar through a Magnetic field
EMF = Blv
Faraday’s law of electromagnetic induction
E=-∆Φ/∆t=(-∆NBA/∆t)
magnetic flux
Φ=NBA=NBAcosθ
thin lens equation
1/f = 1/do + 1/di
snell's law
n₁sinθ₁ = n₂sinθ₂
index of refraction
n = c/v
critical angle
sinθ=n₂/n₁
Thin film(membrane interference
2nt=__λ
total resistance for resistors in series
Rt= R₁ + R₂ + R₃ + ... + Rₙ
total resistance for resistors in parallel
Rt= (R₁⁻¹ + R₂⁻¹ + R₃⁻¹ + ... + Rₙ⁻¹)⁻¹
Charge including time
Q=It
Resistance in a wire of length L and area A
R=ρ(L/A)
Pressure exerted on an area A
P = F/A
absolute pressure
Pabs=P₀+ρgh
gauge pressure
ρgh
Volume flow rate
I=AV
Buoyant force
F=ρVg
Density
ρ=m/v
bernoulli's equation
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Force on a charge q moving parallel to a magnetic field (B)
0 N
Force on a current carrying wire oriented perpendicular to a magnetic field (B)
F=Il×B
capacitance if area of plates is known
C = KεA/d
Electric Potential around a point charge q
V = kq/r
Force on a charge (q) in an Electric field (E)
F = qE
coulomb's law
F = kq₁q₂/r², where k=1/(4πε₀)
charge on a capacitor
Q=CV
Energy stored in a capacitor (3 formulas)
Ucap=½QV=½CV²=½Q²/C
Formula definition of Work
W=F∙d
electric potential energy
Ue= qV
Electric field a distance r from a point charge (q)
F = k|q|/r²
Ohm’s Law
V=IR
Total charge for capacitors in series
Qt=Q₁=Q₂=Q₃
Terminal voltage (Vab) if external resistance (Rext) is known
Vab=I₁Rext
Terminal voltage (Vab) if EMF is known
ε=Vab-I₁R(int)
Voltage across the plates of a capacitor if the E-field is known
Ed=V
Electric Energy (three formulas)
E=VIt=V²Rt=I²Rt
Electric Power
P=VI=V²R=I²R
Force on a charge (q) moving perpendicularly through a magnetic field (B)
F=qv×B
Work to move a point charge (q) a distance r away from another charge (Q)
w=q∆V
Force between two parallel current carrying wires of length l.
F=(µ₀/2π)(I₁I₂l/r) (the third one is L)
Limits of human sight
750 nm-400nm
the wave equation
v=fλ
Magnetic field a distance r from a current carrying wire
B=(µ₀/2π)(I/r)
New wavelength in the original wavelength and the indices of refraction are known
n₁λ₁=n₂λ₂
Change in Heat during an isovolumetric process
Q = nCvΔT
Frequency of a spring mass
f = 1/(2π) * √(k/m)
period of a pendulum
T = 2π√(L/g)
frictional force
F=Fₙµ
frictional force on an incline
mg(cosθ)µ
Acceleration
a= ∆v/∆t
average speed
s = d/t
velocity
v= ∆x/∆t
Average Velocity of a molecule of gas
v = √(3kT/m)
Change in internal energy during a cyclic process
ΔU = 0 J
First Law of thermodynamics
ΔU = ∆Q + ∆W
Acceleration of a mass sliding UP an incline, with friction
a = gsinθ + gμcosθ
Acceleration of a mass sliding DOWN an incline, with friction
a = gsinθ - gμcosθ
Heat required to raise the temperature of a substance
Q = mcΔT
Heat required to vaporize a substance
Q = mLv
Heat required to melt a substance
Q = m(Lf)
Forgotten power equation
P=Fv
Energy of a spring-mass when spring is neither at maximum displacement, nor at the equilibrium point
½kA²=½mv²+½kx²
ideal efficiency
ε=(T_hot - T_cold) / T_hot x100
Newton's second law of motion
F = ma
torque
∑τ=r×F=rFsinθ
Ideal gas law (two equations)
PV = nRT or PV=NKT
Boyle's law
P₁V₁ = P₂V₂
heat of an isobaric process
Q = nCpΔT
work (thermodynamics)
W = -PΔV
internal energy of an ideal gas
U = (3/2) nRT
actual efficiency
εactual=|∑W|/Qin=|Qin-Qout|/Qin
kinetic energy
KE = ½mv²
Hooke's Law
F = -kx
gravitational potential energy
Ug = mgh or mg∆y
Newton's Law of Universal Gravitation'
F = G (m₁ m₂) / r²
centripetal acceleration
a = v²/r
Acceleration due to gravity at the surface of a planet of mass M and diameter d
g = (G*M) / (d/2)²
momentum
p = mv
impulse (two formulas)
J = Ft or J = mv-mv₀
weight
W or Fg=mg
first kinematic
v = v₀ + at
second kinematic
∆x = v₀t + ½at²
third kinematic
v²=v₀²+2a∆x
beat frequency
f = |f1 - f2|
Length (L) of a string producing the fundamental frequency (f)
L=v/2f
Natural frequency of a closed tube of length l
L=v/4f
Wavelength in an open tube of length l
λ=2L
frequency of a pendulum
f = 1/T = 1/(2π √(l/g))
Velocity of waves on a string if tension is known
v = √(T/(m/l))
period of a spring-mass
T = 2π√(m/k)
charles' law
V₁/T₁ = V₂/T₂
Note
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