Formulas

Density is mass per unit volume
Density = mass / volume

velocity = displacement / time

Force = rate of change of momentum

Momentum = mass . velocity

Power is rate of work done
Power = work / time
Unit of power is watt

Potential energy (P)
PE = m.g.h
m = mass
g = acceleration due to gravity (9.81m/s2)
h = height

Kinetic energy (P)
P = (1/2).m.v2
m = mass
v = velocity

Ohm’s law
V = I . R
V = voltage applied
R = Resistance
I = current

Electric power (P) = (voltage applied) x (current)
P = V . I = I2 . R
V = voltage applied
R = Resistance
I = current

OPTICS
Index of refraction
n = c/v

n – index of refraction
c – velocity of light in a vacuum
v – velocity of light in the given material

Physics formulas for grade 11, grade 12 and under graduates.
Density is mass per unit volume
Density = mass / volume
velocity = displacement / time
Force = rate of change of momentum Momentum = mass . velocity
Power is rate of work done
Power = work / time
Unit of power is watt

Potential energy (P)
PE = m.g.h
m = mass
g = acceleration due to gravity (9.81m/s2)
h = height

Kinetic energy (P)
P = (1/2).m.v2
m = mass
v = velocity
Gravity (Force due to gravity)
Fg : Force of attraction
G : Gravitational constant
M1 : Mass of first object
M2 : Mass of second object

Fg = G M1 M2
r2

Acceleration due to gravity at a depth ‘d’ from earth surface is :

gd = g(1-   d  )
 R

Acceleration due to gravity at height ‘h’ from earth surface is :
h is very much smaller than R

gh = g(1-   2h  )
 R

Escape velocity
Escape velocity from a body of mass M and radius r is
For example if you want to calculate the escape verlocity of sa object from earth then,
M is dmass of earth
r is radius of earth
OPTICS Index of refraction
n = c/v

n – index of refraction
c – velocity of light in a vacuum
v – velocity of light in the given material

Under constant acceleration linear motion
v = final velocity
u = intitial velocity
a = acceleration
t = time taken to reach velocity v from u
s = displacement

v = u + a t

s = ut + (1/2)a t 2

s = vt – (1/2)a t 2

v2 = u2 + 2 a s

Friction force (kinetic friction)
When the object is moving then Friction is defined as :
Ff = μ Fn
where
Ff = Friction force, μ= cofficient of friction
Fn = Normal force
Linear Momentum
Momentum = mass x velocity
Capillary action
The height to which the liquid can be lifted is given by:

h =  2γcosθ
ρgr

γ: liquid-air surface tension(T)(T=energy/area)
θ: contact angle
ρ: density of liquid
g: acceleration due to gravity
r: is radius of tube

Simple harmonic motion
Simple harmonic motion is defined by:
d2x/dt2 = – k x
Time period of pendulum
Waves

f = 1
T

ω = 2 π
T

v = f . λ
where
ω = Angular frequency, T=Time period, v = Speed of wave, λ=wavelength

Doppler effect Relationship between observed frequency f and emitted frequency f0:

f = f0 v  )
v + vs

where,
v=velocity of wave
vs=velocity of source. It is positive if source of wave is moving away from observer. It is negative if source of wave is moving towards observer.

Resonance of a string

frequency = f =  nv
2L

where,
L: length of the string
n = 1, 2, 3…

Resonance of a open tube of air(approximate)

Approximate frequency = f =  nv
2L

where,
L: length of the cylinder
n = 1, 2, 3…
v = speed of sound

Resonance of a open tube of air(accurate)

frequency = f =  nv
2(L+0.8D)

where,
L: length of the cylinder
n: 1, 2, 3…
v: speed of sound
d:diameter of the resonance tube

Resonance of a closed tube of air(approximate)

Approximate frequency = f =  nv
4L

where,
L: length of the cylinder
n = 1, 2, 3…
v = speed of sound

Resonance of a closed tube of air(accurate)

frequency = f =  nv
4(L+0.8D)

where,
L: length of the cylinder
n: 1, 2, 3…
v: speed of sound
d:diameter of the resonance tube

intensity of sound

intensity of sound =  Sound Power
area

intensity of sound in decibel= 10log10  I
I0

dB = 10log10  I
I0

where
I=intensity of interest in Wm-2
I0=intensity of interest in 10-12Wm-2

Bragg’s law
nλ = 2d sinθ where
n = integer (based upon order)
λ = wavelength
d = distance between the planes
θ = angle between the surface and the ray
de Broglie equation

λ =  h  =  h
p mv

where
p = momentum
λ = wavelength
h = Planck’s constant
v = velocity

Relation between energy and frequency
E = hν
where
E = Energy
h = Planck’s constant
ν = frequency
Davisson and Germer experiment

λ =  h  
 

where
e = charge of electron
m = mass of electron
V = potential difference between the plates thru which the electron pass
λ = wavelength

Centripetal Force (F)

F = m v2 = m ω2 r
r

Circular motion formula v = ω r

Centripetal acceleration (a) =  v2
r

Torque (it measures how the force acting on the object can rotate the object)
Torque is cross product of radius and Force
Torque = (Force) X (Moment arm) X sin θ
T = F L sin θ
whete θ = angle between force and moment arm
Forces of gravitation
F = G (m1.m2)/r2
where G is constant. G = 6.67E – 11 N m2 / kg2
Stefan-Boltzmann Law
The energy radiated by a blackbody radiator per second = P
P = AσT4
where,
σ = Stefan-Boltzmann constant
σ = 5.6703 × 10-8 watt/m2K4
Efficiency of Carnot cycle

η =  1 –  Tc
Th

Ideal gas law
P V = n R T
P = Pressure (Pa i.e. Pascal)
V = Volume (m3)
n = number of of gas (in moles)
R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )
T = Temperatue ( in Kelvin [K])
Boyles law (for ideal gas)
P1 V1 = P2V2
T (temperature is constant)
Charles law (for ideal gas)

V1 = V2
T1 T2

P (pressure is constant)

Translational kinetic energy K per gas molecule (average molecular kinetic energy:)

K = 3 k T
2

k = 1.38066 x 10-23 J/K Boltzmanns constant

Internal energy of monoatomic gas

K = 3 n R T
2

n = number of of gas (in moles)
R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )

Root mean square speed of gas

V2rms = 3 k T
m

k = 1.38066 x 10-23 J/K Boltzmanns constant
m = mass of gas

Ratio of specific heat (γ)

γ = Cp
Cv

Cp = specific heat capacity of the gas in a constant pressure process
Cv = specific heat capacity of the gas in a constant volume process

Internal entergy of ideal gas Internal entergy of ideal gas (U) = cv nRT
In Adiabatic process no heat is gained or lost by the system.
Under adiabetic condition PVγ = Constant
TVγ-1 = Constant
where γ is ratio of specific heat.

γ = Cp
Cv

Boltzmann constant (k)

k = R
Na

R = gas constant
Na = Avogadro’s number.

Speed of the sound in gas

R = gas constant(8.314 J/mol K)
T = the absolute temperature
M = the molecular weight of the gas (kg/mol)
γ = adiabatic constant = cp/cv
Capillary action
The height to which the liquid can be lifted is given by
h=height of the liquid lifted
T=surface tension
r=radius of capillary tube

h=  2T
ρrg

Resistance of a wire

R =  ρL
A

ρ = rsistivity
L = length of the wire
A = cross-sectional area of the wire

Ohm’s law
V = I . R
V = voltage applied
R = Resistance
I = current

Electric power (P) = (voltage applied) x (current)
P = V . I = I2 . R
V = voltage applied
R = Resistance
I = current

Resistor combination
If resistors are in series then equivalent resistance will be
Req = R1 + R2 + R3 + . . . . . . + Rn
If resistors are in parallel then equivalent resistance will be
1/Req = 1/R1 + 1/R2 + 1/R3 + . . . . . . + 1/Rn
In AC circuit average power is :
Pavg = VrmsIrms cosφ
where,
Pavg = Average Power
Vrms = rms value of voltage
Irms = rms value of current
In AC circuit Instantaneous power is :
PInstantaneous = VmIm sinωt sin(ωt-φ)
where,
PInstantaneous = Instantaneous Power
Vm = Instantaneous voltage
Im = Instantaneous current
Capacitors
Q = C.V
where
Q = charge on the capacitor
C = capacitance of the capacitor
V = voltage applied to the capacitor
Total capacitance (Ceq) for PARALLEL Capacitor Combinations:
Ceq = C1 + C2 + C3 + . . . . . . + Cn
Total capacitance (Ceq) for SERIES Capacitor Combinations:
1/Ceq = 1/C1 + 1/C2 + 1/C3 + . . . . . . + 1/Cn
Parallel Plate Capacitor

C = κ ε0   A 
d

where
C = [Farad (F)]
κ = dielectric constant
A = Area of plate
d = distance between the plate
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)

Cylindrical Capacitor

C = 2 π κ ε0 L
ln (b/a)

where
C = [Farad (F)]
κ = dielectric constant
L = length of cylinder [m]
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)

Spherical Capacitor

C = 4 π κ ε0 a b
b – a

where
C = [Farad (F)]
κ = dielectric constant
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)

Magnetic force acting on a charge q moving with velocity v
F = q v B sin θ
where
F = force acting on charge q (Newton)
q = charge (C)
v = velocity (m/sec2)
B = magnetic field
θ = angle between V (velocity) and B (magnetic field)
Force on a wire in magnetic field (B)
F = B I l sin θ
where
F = force acting on wire (Newton)
I = Current (Ampere)
l = length of wire (m)
B = magnetic field
θ = angle between I (current) and B (magnetic field)
In an RC circuit (Resistor-Capacitor), the time constant (in seconds) is:
τ = RC
R = Resistance in Ω
C = Capacitance in in farads.
In an RL circuit (Resistor-inductor ), the time constant (in seconds) is:
τ = L/R
R = Resistance in Ω
C = Inductance in henries
Self inductance of a solenoid = L = μn2LA
n = number of turns per unit length
L = length of the solenoid.
Mutual inductance of two solenoid two long thin solenoids, one wound on top of the other
M = μ0N1N2LA
N1 = total number of turns per unit length for first solenoid
N2 = number of turns per unit length for second solenoid
A = cross-sectional area
L = length of the solenoid.
Energy stored in capacitor

E = 1 C V 2
2

Coulomb’s Law
Like charges repel, unlike charges attract.
F = k (q1 . q2)/r2
where k is constant. k = 1/(4 π ε0) ≈ 9 x 109 N.m2/C2
q1 = charge on one body
q2 = charge on the other body
r = distance between them Calculator based upon Coulomb’s Law
Ohm’s law
V = IR
where
V = voltage
I = current
R = Resistence
Electric Field around a point charge (q)
E = k ( q/r2 )
where k is constant. k = 1/(4 π ε0) ≈ 9 x 109 N.m2/C2
q = point charge
r = distance from point charge (q)
Electric field due to thin infinite sheet

E = σ
2 ε0

where
E = Electric field (N/C)
σ = charge per unit area C/m2
ε0 = 8.85 X 10-12 C2/N m2

Electric field due to thick infinite sheet

E = σ
ε0

where

E = Electric field (N/C)
σ = charge per unit area C/m2
ε0 = 8.85 X 10-12 C2/N m2

Magnetic Field around a wire (B) when r is greater than the radius of the wire.

B = μ0 I
2 π r

where
I = current
r = distance from wire
and r ≥ Radius of the wire

Magnetic Field around a wire (B) when r is less than the radius of the wire.

B = μ0 I r
2 π R2

where
I = current
R = radius of wire
r = distance from wire
and r ≤ Radius of the wire (R)

Magnetic Field At the center of an arc

B = μ0 I φ
4 π r

where
I = current
r = radius from the center of the wire

Bohr’s model

L =  nh
2 π

where
L = angular momentum
n = principal quantum number = 1,2,3,…n
h = Planck’s constant.

Emitting Photons(Rydberg Formula)

Ephoton = E0 1  –  1  )
n12 n22

where
n1 < n2
E0 = 13.6 eV

Half life of radioactive element

t1/2 ln(2)
λ

Average life of radioactive element

τ =  1
λ

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