PHYS 2300 and 2305: General Physics I and II Formulas
Chapter 1
Chapter 2
Trig Formulas
sin π =Opposite
Hypotenuse π = sinβ1 (
Opposite
Hypotenuse )
cos π =Adjacent
Hypotenuse π = cosβ1 (
Adjacent
Hypotenuse )
tan π =Oppostie
Adjacent π = tanβ1 (
Oppostie
Adjacent)
π2 = π2 + π2
Velocity
Average Velocity π£ =πππ πππππππππ‘
π‘πππ=
βοΏ½οΏ½
βπ‘ ππ π£ =
βοΏ½οΏ½
βπ‘ 2.2
Average Speed ππ£πππππ π ππππ =πππ π‘ππππ
π‘πππ 2.1
Instantaneous Velocity π£ = limβπ‘β0
βοΏ½οΏ½
βπ‘ 2.3
Vectors
Vector Addition by Components
π΄ + οΏ½οΏ½ = πΆ Where
πΆπ₯ = π΄π₯
+ π΅π₯
πΆπ¦ = π΄π¦
+ π΅π¦
Then to find πΆ use π2 = π2 + π2
Acceleration
Average Acceleration οΏ½οΏ½ =βπ£
βπ‘ 2.4
Instantaneous Acceleration π = lim
βπ‘β0
βοΏ½οΏ½
βπ‘ 2.5
Motion of a particle with constant acceleration
π£ = π£0 + ππ‘ 2.4
π₯ =1
2(π£0 + π£)π‘ or π =
1
2(π£0 + π£)π‘ 2.7
π₯ = π£0π‘ +1
2ππ‘2 Or π = π£0π‘ +
1
2ππ‘2 2.8
π£2 = π£02 + 2ππ₯ or π£2 = π£0
2 + 2ππ 2.9
Chapter 3
Chapter 4
Average Velocity/Acceleration
Average Velocity π£ =βοΏ½οΏ½
βπ‘ ππ π£ =
βοΏ½οΏ½
βπ‘ 2.2
Average Acceleration οΏ½οΏ½ =βπ£
βπ‘ 2.4
Projectile Motion
X direction Y direction
π£π₯ = π£0π₯ + ππ₯π‘ π£π¦ = π£0π¦ + ππ¦π‘
ππ π£π¦ = π£0π¦ + ππ‘
3.3
π₯ =1
2(π£0π₯ + π£π₯)π‘
or π =1
2(π£0π₯ + π£π₯)π‘
π¦ =1
2(π£0π¦ + π£π¦)π‘
or β =1
2(π£0π¦ + π£π¦)π‘
3.4
π₯ = π£0π₯π‘ +1
2ππ₯π‘2
or π = π£0π₯π‘ +1
2ππ₯π‘2
π¦ = π£0π¦π‘ +1
2ππ¦π‘2
or β = π£0π¦π‘ +1
2ππ‘2
3.5
π£π₯2 = π£ππ₯
2 + 2ππ₯π₯ or π£π₯
2 = π£ππ₯2 + 2ππ₯π
π£π¦2 = π£ππ¦
2 + 2ππ¦π¦
or π£π¦2 = π£ππ¦
2 + 2πβ
3.6
Relative Motion
π£π΄πΆ = π£π΄π΅ + π£π΅πΆ π£π΄π΅ = βπ£π΅π΄
Newtonβs Second Law
General Ξ£οΏ½οΏ½ = ποΏ½οΏ½
4.1
Component form Ξ£πΉπ₯ = πππ₯ Ξ£πΉπ¦ = πππ¦
4.2
Gravitational Force
Gravitational Force
πΉ = πΊπ1π2
π2
4.3
Weight
W=mg
Where π = πΊπ1
π2
G=Universal Gravitational Constant =6.67π₯10β11 ππ2/ππ2
Friction Static Friction (maximum)
ππ πππ₯ = ππ πΉπ 4.7
Kinetic Frictional ππ = πππΉπ 4.8
Chapter 5
Chapter 6
Speed π£ =2ππ
π 5.1
Centripetal Acceleration ππ =
π£2
π 5.2
Centripetal Force πΉπ =ππ£2
π 5.3
Banked Curve π‘πππ =π£2
ππ 5.4
Satellites in circular orbits
π£ = βπΊππΈ
π
π =2ππ3/2
βπΊππΈ
5.5 5.6
NOTE:
ME mass of earth = 5.98x1024kg rE radius of earth 6.38x106m G=6.67x10-11 NΒ·m2/kg2
Vertical Circular Motion
1) πΉπ = πΉπ β ππ =ππ£2
π
2) πΉπ = πΉπ =ππ£2
π
3) πΉπ = πΉπ + ππ =ππ£2
π
4) πΉπ = πΉπ =ππ£2
π
Fig. 5.20
Work done by constant Force
π = (πΉπππ π)π ππ
π = (πΉπππ π)π 6.1
Kinetic Energy πΎπΈ =1
2ππ£2 6.2
Work-Energy Theorem
π = πΎπΈπ β πΎπΈ0
=1
2ππ£π
2 β1
2ππ£0
2
=1
2π(π£π
2 β π£02)
6.3
Work done by gravity πππππ£ππ‘π¦ = ππ(β0 β βπ) 6.4
Gravitational Potential Energy
ππΈ = ππβ 6.5
Alternative Work-Energy Theorem
πππ = πΈπ β πΈ0
= (πΎπΈπ + ππΈπ) β (πΎπΈ0 + ππΈ0) 6.8
When πππ = 0 πΈπ = πΈ0 or
(πΎπΈπ + ππΈπ) = (πΎπΈ0 + ππΈ0)
Power π =π
π‘=
βπΈ
π‘= πΉπ£
6.10 6.11
Work done by a variable Force
Area under the curve of a πΉπππ π vs. s graph
Conservative Forces: force of gravity, spring force
Non-conservative forces: friction, air resistance
Chapter 7
Chapter 8
Impulse and Momentum
Impulse π½ = οΏ½οΏ½βπ‘ 7.1
Linear Momentum, p p=mv 7.2
Impulse-Momentum Theorem
(β οΏ½οΏ½) βπ‘ = ππ£π β ππ£0 = πβπ£
Or J=Ξp 7.4
Collision
Final Velocity of 2 objects in a head-on collision where one object is initially at rest 1: moving object 2: object at rest
π£π1 = (π1 β π2
π1 + π2) π£01
π£π2 = (2π1
π1 + π2) π£01
7.8
Conservation of Linear Momentum (in 1D)
οΏ½οΏ½0 = οΏ½οΏ½π
οΏ½οΏ½0 = οΏ½οΏ½π β οΏ½οΏ½0 = 0 7.7
Elastic Collision π1π£01 + π2π£02 = π1π£π1 + π2π£π2 7.7b
Inelastic Collision π1π£01 + π2π£02 = (π1 + π2)π£π
Conservation of Linear Momentum (in 2D)
π1π£01π₯ + π2π£02π₯ = π1π£π1π₯ + π2π£π2π₯
π1π£01π¦ + π2π£02π¦ = π1π£π1π¦ + π2π£π2π¦ 7.9
Center of Mass
Center of mass location
π₯ππ =π1π₯1 + π2π₯2
π1 + π2 7.10
Center of mass velocity
π£ππ =π1π£1 + π2π£2
π1 + π2 7.11
Angular displacement
Ξπ = π β π0
π =π
π
8.1
Average angular velocity οΏ½οΏ½ =
βπ
βπ‘ 8.2
Average angular acceleration οΏ½οΏ½ =
βπ
βπ‘ 8.4
Motion of a particle with constant acceleration
π = π0 + πΌπ‘ 8.4
π =1
2(π + π0)π‘ 8.6
π = π0π‘ +1
2πΌπ‘2 8.7
π2 = π02 + 2πΌπ 8.8
Relationship between angular variables and tangential variables (t subscript)
π£π = ππ ππ = ππΌ
8.9 8.10
When no slipping π£ = π£π = ππ π = ππ = ππΌ
8.12 8.13
Centripetal acceleration ππ = ππ2 8.11
Chapter 9
Moments of Inertia I for various rigid objects of Mass M
Torque and Inertia
Torque π
π = πΉβ 9.1
When at Equilibrium β π = 0 9.2
Moment of Inertia
πΌ = β ππ2 9.6
Newtonβs Second Law for a rigid body rotating about a Fixed axis
β π = πΌπΌ
9.7
Work, Energy
Rotational work ππ = ππ 9.8
Rotational Kinetic Energy πΎπΈπ =
1
2πΌπ2 9.9
Angular Momentum πΏ = πΌπ 9.1
Center of Gravity π₯ππ =π1π₯1 + π1π₯1 + β―
π1 + π2 + β― 9.2
See reverse side for moments of Inertia I for various rigid objects of Mass M
Thin walled hollow cylinder or hoop
πΌ = ππ 2
Solid cylinder or disk
πΌ =1
2ππ 2
Thin rod, axis perpendicular to rod and passing though center
πΌ =1
12ππΏ2
Thin rod, axis perpendicular to rod and passing though end
πΌ =1
3ππΏ2
Solid Sphere, axis through center
πΌ =2
5ππ 2
Solid Sphere, axis tangent to surface
πΌ =7
5ππ 2
Thin Walled spherical shell, axis through center
πΌ =2
3ππ 2
Thin Rectangular sheet, axis along one edge
πΌ =1
3ππΏ2
Thin Rectangular sheet, axis parallel to sheet and passing though center of the other edge
πΌ =1
12ππΏ2
Chapter 10
Force Applied πΉπ₯πππππππ
= ππ₯ 10.1
Hookeβs Law πΉπ₯ = βππ₯ 10.2
Frequency cycles per time π =
1
π 10.5
Angular frequency
π = 2ππ = 2ππβ 10.6
Maximum Velocity Simple Harmonic Motion
π£πππ₯ = π΄π 10.8
Maximum Acceleration Simple Harmonic Motion
ππππ₯ = π΄π2 10.11
Angular frequency of simple harmonic motion
π = βππβ 10.11
Elastic potential energy
ππΈππππ π‘ππ =1
2ππ₯2 10.13
Simple Pendulum (10.16)
Angular Frequency
π = βπ
πΏ
Time Period
π = 2πβπΏ
π
Length
πΏ =π2π
4π2
Physical pendulum (10.15)
Angular Frequency
π = βπππΏ
πΌ
Time Period
π = 2πβπΌ
πππΏ
Elastic deformation -stretch and compression (10.17) Perpendicular to Area (A)
Y = constant called Youngβs modulus
Force
πΉ = π (ΞπΏ
πΏ0) π΄
Change in Length
ΞπΏ =πΉπΏ0
ππ΄
Shear Deformation (change in shape)
Parallel to Area (A) S = constant called the shear modulus
Force
πΉ = π (Ξπ
πΏ0) π΄
Change in Length
ΞX =πΉπΏ0
ππ΄
Pressure (related to Volume deformation)
π =πΉ
π΄ 10.19
change in pressure needed to change the volume
B = constant known as the bulk modulus When the volume decreases, βπ is negative
βπ = βπ΅ (βπ
ππ) 10.20
Chapter 11
Chapter 12
Density π =π
π 11.1
Pressure
π =πΉ
π΄ 11.3
Specific Gravity =π·πππ ππ‘π¦ ππ π π’ππ π‘ππππ
1.000 Γ 103 ππ/π3 11.2
Pressure and depth
in a static Fluid
P1 is higher than P2 π2 = π1 + ππβ 10.4
Gauge Pressure ππβ
Archimedesβ
principle πΉπ΅ = ππππ’ππ 11.6
Mass Flow Rate πππ π ππππ€ πππ‘π = ππ΄π£ 11.7
Volume flow rate π = π΄π£ =π
π‘
Bernoulliβs Equation π1 +1
2ππ£1
2 + πππ¦1 = π2 +1
2ππ£2
2 + πππ¦2 11.11
Equation of
continuity π1π΄1π£1 = π2π΄2π£2 11.8
equation of
continuity ( ) π΄1π£1 = π΄2π£2
Force to move
Viscous Layer with
constant velocity
πΉ =ππ΄π£
π¦ 11.13
Poiseuilleβs law π =ππ 4(π2 β π1)
8ππΏ 11.14
Force and Area if
Pressure same πΉ1/π΄1 = πΉ2/π΄2 ππ πΉ2 = πΉ1 (
π΄2
π΄1)
Temperature Scales
Fahrenheit to Celsius
πΆ =
5
9(πΉ β 32)
Celsius to Fahrenheit
πΉ =
9
5πΆ + 32
Celsius to Kelvin K=C+273.15 or π =
ππ + 273.15 12.1
Thermal Expansion
Linear Thermal Expansion
βπΏ = πΌπΏπβπ 12.2
Volume Thermal Expansion
βπ = π½π0βπ 12.3
Heat and Power
Heat and temperature change
βπ = ππβπ 12.4
Heat and phase change π = ππΏ 12.5
% Relative Humidity ππππ‘πππ ππ€ππ‘ππ π£ππππ‘
πΈππ’ππππππ’π ππ€ππ‘ππ π£ππππ‘ @ π‘πππ 12.6
Chapter 13
Heat and Power
Power P=Q/t
Heat Conducted π =(ππ΄βπ)π‘
πΏ 13.1
Radiant energy
e emissivity π = 5.67x10-8 J/(s*m2*K4) T temp in Kelvins A surface area
π = πππ4π΄π‘
Net radiant Power
T object Temp in kelvins To environment temp in Kelvins
ππππ‘ = πππ΄(π4 β π04) 13.3
Chapter 14
Molecular Mass, Moles, and Avogadroβs Number
Atomic Mass Unit 1 π’ = 1.6605 Γ 10β27 ππ
Avogadroβs Number ππ΄ = 6.022 Γ 1023 πππβ1
Number of Moles, n N number of particles (atoms or molecules)
π =π
ππ΄
Number of Moles, n m sample mass (g) mass per mole: g/mol
π =π
πππ π πππ ππππ
Mass of a particle πππππ‘ππππ =πππ π πππ ππππ
ππ΄
Density π =π β πππ π πππ ππππ
π
Ideal Gas Law
Ideal Gas law n number of moles R Universal gas constant =8.31 J/(mol *K) T temp kelvins
ππ = ππ π 14.1
Ideal Gas Law (alternative form) N number of particles k Boltzmannβs constant (1.38x10-23 J K-1)
ππ = πππ 14.2
Boyleβs and Charlesβ Laws
Boyleβs law (when n and T are constant)
ππππ = ππππ 14.3
Charlesβ law
(n and P are constant)
ππ
ππ=
ππ
ππ 14.4
Energy
Average Kinetic Energy for a molecule πΎπΈ =
1
2ππ£πππ
2 =3
2ππ 14.6
Internal Energy π =3
2ππ π 14.7
Diffusion
Fickβs law of diffusion D Diffusion constant ΞC is the solute concentration difference between the ends of the channel (same as density)
π =π·π΄βπΆπ‘
πΏ 14.8
Chapter 15
First Law of Thermodynamics
First Law Ξπ = ππ β π0 = π β π 15.1
Note: βπ Change in Internal Energy Q (heat) is positive when the system gains heat and negative when it loses heat. W (work) is positive when work is done by the system and negative when work is done on the system.
Monatomic Ideal Gas Internal Energy *R=8.31 J/(mol K)
π =3
2ππ π 12.5
Applications of First Law
Process Work Done First Law
Isobaric
(constant pressure)
π = π(ππ β ππ)
(Eq 15.2) βπ = π β π(ππ β ππ)
(π =5
2ππ βπ)
Isochoric
(constant volume) W=0 J βπ = π β 0π½
(π =3
2ππ βπ)
Isothermal (constant temp)
π = ππ πππ(ππ
ππ)
(Eq. 15.3)
ππ½ = π β ππ πππ(ππ
ππ)
Adiabatic (no heat flow)
π =3
2ππ (ππ β ππ)
(15.4)
βπ = 0π½ β3
2ππ (ππ β ππ)
Adiabatic expansion/compression of an ideal gas
π0π0πΎ
= πππππΎ 15.5
Heat with known number of moles
π = πΆπΞπ 15.6
molar specific heat πΆπ =
5
2π
πΆπ£ =3
2π
15.7 15.8
Heat Engines
The efficiency e of a heat engine
π =ππππ ππππ
πΌπππ’π‘ βπππ‘=
|π|
|ππ»|= 1 β
|ππ|
|ππ»|
15.11 15.13
Conservation of energy requires
|ππ»| = |π| + |ππ| 15.12
Carnot Engine
For a Carnot engine
|ππΆ|
|ππ»|=
|ππΆ|
|ππ»| 14.14
Efficiency e for a Carnot engine
πππππππ‘ = 1 βππΆ
ππ» 15.15
Coefficient of Performance (COP)
COP of a refrigerator or an air conditioner
πΆππ =|ππ|
|π|=
1
ππ»ππΆ
β 1
COP of a heat pump πΆππ =|ππ»|
|π| 15.17
Entropy
change in entropy Ξπ = (π
π)
π 15.18
change in entropy βπΊπππππππππ
βππ’πππ£πππ ππ = βππ π¦π π‘ππ + βππ π’ππππ’ππππππ
=βπππππ + βππ»ππ‘
Energy unavailable for doing work
ππ’πππ£πππππππ = π0Ξππ’πππ£πππ π 15.19
Chapter 16
Waves
Speed of a Wavelength π£ = ππ =π
π 16.1
Speed of a wave on a
string π£ = β
πΉ
π/πΏ 16.2
description +x direction
π¦ = π΄π ππ(2πππ‘ β2ππ₯
π) 16.3
description -x direction
π¦ = π΄π ππ(2πππ‘ +2ππ₯
π) 16.4
Speed of Sound
Speed of Sound in a Gas k= 1.38x10-23
π£ = βπΎππ
π 16.5
Speed of sound in a liquid
π£ = βπ΅ππ
π 16.6
Speed of sound in solid bar
π£ = βπ
π 16.7
Sound Intensity
Intensity πΌ =π
π΄ 16.8
Intensity -uniform in all directions
πΌ =π
4ππ2 16.9
Intensity level in decibels I0 =1x10-12W/m2
π½ = (10ππ΅) log (πΌ
πΌπ) 16.10
Doppler Effect
Source Moving toward stationary observer
ππ = ππ (1
1 βπ£π π£
) 16.15
Source Moving away from stationary observer
ππ = ππ (1
1 +π£π π£
) 16.15
Observer moving toward stationary source
ππ = ππ (1 +π£π
π£) 16.15
Observer moving away from stationary source
ππ = ππ (1 βπ£π
π£) 16.15
Chapter 17
Chapter 18
Constructive and Destructive Interference
Constructive 2 waves in Phase
Difference in path lengths is zero or an integer (0,1,2,3β¦)
Destructive 2 waves in Phase
Difference in path lengths is a half- integer (0.5,1.5,2.5,β¦)
Constructive 2 waves out of Phase
Difference in path lengths is a half- integer (0.5,1.5,2.5,β¦)
Destructive 2 waves out of Phase
Difference in path lengths is zero or an integer (0,1,2,3β¦)
Diffraction
Single Slit βfirst minimum π πππ =π
π· 17.1
Circular Opening βfirst minimum π πππ = 1.22π
π· 17.2
beats πππππ‘ = π1 β π2 17.46
Standing Waves
Transverse Natural frequency Fixed at both ends
ππ = π (π£
2πΏ) for n=1,2,β¦ 17.3
Longitudinal Natural frequency open at both ends
ππ = π (π£
2πΏ) for n=1,2,β¦ 17.4
Longitudinal Natural frequency open at one end
ππ = π (π£
4πΏ) for n=1,3,5,β¦ 17.5
Formulas Number of
electrons/protons # =
π
π
Coulombs law: F=force
Where one exerts on
two
πΉ =π|π1||π2|
π2 18.1
Electric Field οΏ½οΏ½ =οΏ½οΏ½
π0 18.2
Magnitude of Electric Field πΈ =
π|π|
π2 18.3
Magnitude of Electric Field for a parallel plate capacitor
πΈ =π
π0π΄=
π
π0 18.4
Electric Flux Ξ¦πΈ = β(πΈ cos π)Ξπ΄ =π
π0 18.6,7
Important Numbers
π = 8.99 Γ 109 π β π2/πΆ2
Permittivity of free space
π0 = 8.85 Γ 10β12 πΆ2
π β π2
Magnitude of charge on electron (-e) or proton (+e) π = 1.6 Γ 10β19 C (a lot of time π0)
Mass of Electron 9.11 Γ 10β31 ππ
Mass of Proton 1.673 Γ 10β27 ππ
Mass of Neutron 1.675 Γ 10β27 ππ
Chapter 19
Chapter 20
Work and Electric
Potential Energy ππ΄π΅ = πΈππΈπ΄ β πΈππΈπ΅ 19.1
Electric Potential π =πΈππΈ
π0=
ππ
π 19.3,6
Electric Potential Difference Charge moves from A to B
ππ΄ β ππ΅ =πΈππΈπ΅
π0β
πΈππΈπ΄
π0=
βππ΄π΅
π0 19.4
Electric Potential Difference Charge moves from B to A
ππ΅ β ππ΄ =ππ΄π΅
π0
Total Energy πΈ =1
2ππ£2 +
1
2πΌπ2 + ππβ +
1
2ππ₯2
+ πΈππΈ
Electric field πΈ = ββπ
βπ 19.7a
Charge on each plate of a capacitor
π = πΆπ
Dielectric constant (Eβs are electric fields without and with a dielectric)
π =πΈπ
πΈ
Capacitance of a parallel plate capacitor πΆ =
π π0π΄
π
Electric Potential Energy Stored in a capacitor
πΈπππππ¦ =1
2ππ =
1
2πΆπ2 =
π2
2πΆ 19.11
Energy Density Energy Density =πΈπππππ¦
ππππ’ππ=
1
2π π0πΈ2 19.12
Current (if electric
current is constant) πΌ =βπ
βπ‘ 20.1
Ohms Law π = πΌπ ππ π =π
πΌ ππ πΌ =
π
π 20.2
Resistance with length L, cross-sectional area A
π = ππΏ
π΄ 20.3
Resistance and Resistivity (T temp)
π = π0[1 + πΌ(π β π0)] π = π 0[1 + πΌ(π β π0)]
20.4,5
Electric Power π = πΌπ, π = πΌ2π , π =π2
π 20.6
AC Circuits π = π0sin (2πππ‘) πΌ = πΌ0sin (2πππ‘)
20.7,8
RMS Formulas with Current and Voltage
πΌπππ =πΌ0
β2
ππππ =π0
β2
20.12 20.13
Average Power
οΏ½οΏ½ = πΌπππ ππππ οΏ½οΏ½ = πΌπππ
2 π
οΏ½οΏ½ =ππππ
2
π
20.15
Series (I is the same)
π π = π 1 + π 2 + π 3 + β― 1
πΆπ =
1
πΆ1+
1
πΆ2+
1
πΆ3+ β―
20.16 20.19
Parallel (V is the same)
1
π π =
1
π 1+
1
π 2+
1
π 3+ β―
πΆπ = πΆ1 + πΆ2 + πΆ3 + β―
20.17 20.18
RC circuits π = π0[1 β π
βπ‘
π πΆ] (charging) π = π πΆ
π = π0πβπ‘
π πΆ (discharging)
20.20 20.21 20.22
Chapter 21
Chapter 22
Magnitude of magnetic
Field π0 = 4π Γ 10β7 π β π/π΄
π΅ =πΉ
|π0|π£ sin π
π΅ =π0πΌ
2ππ
π΅ = ππ0πΌ
2π
π΅ = π0ππΌ
21.1 21.5 21.6 21.7
Radius of circular path of particle caused by F
π =ππ£
|π|π΅ 21.2
Relationship between Mass and B π = (
ππ2
2π)
2
π΅2
Force on a current in a magnetic field
πΉ = πΌπΏπ΅π πππ 21.3
Torque on a current-carrying coil
π = ππΌπ΄π΅π πππ π is the angle between direction of B and the normal plane
21.4
Ampereβs Law β π΅||βπ = π0πΌ 21.8
RHR 1: Fingers point along the direction of οΏ½οΏ½ and the thumb points along the
velocity οΏ½οΏ½ The palm of the hand then faces in the direction of οΏ½οΏ½ that acts on a positive charge. RHR 2: Curl the fingers of the right hand into a half-circle. Point the thumb in the direction of the conventional current I, and the tips of the fingers will
point in the direction of οΏ½οΏ½
Motional emf β° = π£π΅πΏ 22.1
Magnetic Flux Ξ¦ = π΅π΄πππ π 22.2
Faradayβs Law β° = βπβΞ¦
βπ‘ 22.3
Emf induced ion a
rotating planar coil
π = 2ππ β° = ππ΄π΅π sin(ππ‘) = β°0 sin(ππ‘) 22.4
Current πΌ =π β β°
π 22.5
Mutual Inductance π =ππ Ξ¦π
πΌπ 22.6
Emf due to mutual
inductance β°π = βπΞπΌπ
Ξπ‘ 22.7
Self-Inductance πΏ =πΞ¦
πΌ 22.8
Emf due to self-
inductance β°π = βπΏ
ΞπΌ
Ξπ‘ 22.9
Energy stored in an
inductor πΈπππππ¦ =
1
2πΏπΌ2 22.10
Energy Density πΈπππππ¦ π·πππ ππ‘π¦ =1
2π0π΅2 22.11
Voltage and turns of
primary and secondary
coil
ππ
ππ=
ππ
ππ 22.12
Current and turns of
primary and secondary
coil
πΌπ
πΌπ=
ππ
ππ 22.13
Power Power=Energy*time
Chapter 23
Chapter 24
Rms Voltage across a
capacitor ππππ = πΌπππ ππ 23.1
Capacitive Reactance ππΆ =1
2πππΆ 23.2
Rms Voltage across an
inductor ππππ = πΌπππ ππΏ 23.3
Inductive Reactance ππΏ = 2πππΏ 23.4
Rms Voltage for
circuit containing
resistance, capacitance,
and inductance
ππππ = πΌπππ π 23.6
Impedance of a
resistor, capacitor and
inductor connected in a
series
π = βπ 2 + (ππΏ β ππΆ)2 23.7
Tangent of the phase
angle π‘πππ =
ππΏ β ππΆ
π 23.8
Average Power οΏ½οΏ½ = πΌπππ ππππ πππ π 23.9
Resonant frequency π0 =1
2πβπΏπΆ 23.10
Power Factor πππ€ππ ππππ‘ππ =R
π
Speed of Light π = 3.00 Γ 108 π/π
Speed of Light in a
vacuum π =
1
βπ0π0
24.1
Total energy density
π’ =1
2π0πΈ2 +
1
2π0π΅2
π’ = π0πΈ2
π’ =1
π0π΅2
24.2
Relationship between
magnitudes Electric
and magnetic field
waves
πΈ = ππ΅ 2.43
Rms for Electric Field πΈπππ =1
β2πΈ0
Rms for Magnetic
Field π΅πππ =
1
β2π΅0
Intensity π = ππ 24.4
Doppler Effect in
vacuum
+ come together
- move apart
ππ = ππ (1 Β±π£πππ
π) 24.6
Marlusβ Law π = π0πππ 2π 24.7
Chapter 25
Concave Mirror
Focal length Concave
mirror π =
1
2π 25.1
Focal length Convex Mirror
π = β1
2π 25.2
Mirror Equation 1
ππ+
1
ππ=
1
π 25.3
Magnification
Equation
π = βππ
ππ
π =βπ
βπ
25.4
Plain Mirror
Forms an upright virtual image
Image located same distance behind the mirror as the object in front
Heights of object and virtual image the same
Information for Spherical mirrors
Focal Length + Concave mirror
- Convex mirror
Object distance + Object in front (real)
- Object behind (virtual)
Image Distance + Image in front (real)
- Image behind (virtual)
Magnification (sign) + Image is upright
- Image is inverted
Magnification (magnitude)
>1 larger
<1 smaller
Revised 5/30/18