Files/Other

• PHY1&2 Toolbox / "Cheatsheet"

• PHY 202 Syllabus   -   Free Online Textbook

• PHY 222 Syllabus   -   Free Online Textbook:   Vol1   Vol2   Vol3

• Practice Test Problems -  examples of the kinds of questions on the tests, or review for the final.

• Spreadsheet Graphing.pdf

• RREF Matrix directions

• Optics Worksheet

Temp Scales: TF = 9/5 TC + 32    and    TC = 5/9 (TF - 32)   

Thermal Expansion: ΔL = α LO  ΔT   and    ΔV = α VO  ΔT

Sensible Heat:  Q = m c ΔT

Latent Heat:  Q = m L

Mixing Problems: Σ Q = 0 

Conduction: Q / t = k A ΔT / d

Thermal Resistance: R = d / k

Convection: Q / t = h A ΔT

Radiation:  R = P / A = e σ T 4

Ideal Gas Law:  p V = n R T   or    p1 V1  / T1  = p2 V2  / T2  (T in Kelvin, p abs.)

Molecular Energy: KE = 3/2 k T

1st Law of Thermo: Q = ΔU + W

Efficiency: EFF = W / Q  ≈ 1 - TC  / TH   (T in Kelvin)

k = 1.38 x 10 -23 J / K     (Boltzmann's Constant) 

1 kcal = 1000 cal = 4184 J = 3.97 BTU  

F = Electric Force:

  Between two charges:  F = k q1 q2 / r2

E = Electric Field: (unit: 1 N/C or 1 V/m)

  From a point charge:  E = F / q = k q1 / r2

V = Potential Difference (unit: 1 V = 1 J / C): V = W / q

I = Current (unit: 1 A = 1 C/s): I = Q / t

ρ = Resistivity: (unit: 1 Ω m): 

R = Resistance (unit: 1 Ω = 1 V / A): R = ρ L / A  or w/ temp R = Ro(1 + α Δ T)

Ohm's Law: V = I R

Resistors in Series: RTotal = R1 + R2 + ...

Resistors in Parallel: RTotal = (1 / R1 + 1 / R2 + ...)-1

Power (unit: 1 W  = 1 J/C): P = W / t = E /t    or P = IV = I2R = V2 / R

Batteries in Series: VTotal = V1 + V2 + ...

Batteries in Parallel: Voltages should match to avoid killing batteries

Kirchhoff's Rules: Σ I = 0 at a point, Σ V = 0 in a loop

C = Capacitance (unit 1 F = 1 C / V): C = Q / V   or C = k εo A / d 

Capacitors in Parallel: CTotal = C1 + C2 + ...

Capacitors in Series: CTotal = (1 / C1 + 1 / C2 + ...)-1

Energy of a Capacitor: E = 1/2 Q V2 = 1/2 C V2 = 1/2 Q2 / C

Capacitor Charging: Q = Qmax(1 - e-t / Τ )  and I = (V - Q / C) / R  where Τ  = R C and   Qmax = C V

Capacitor Discharging: Q = Qo e-t / Τ 

E Fields of Continuous Objects - 221 Only

E =  ∫ k / r2 dQ

    Rod, d from end: E = k Q / (d (d + L))

    Rod, d above center: E = k Q / d [ 1 / √(d2 + (½ L)2)]

    Ring of rad r, d on axis: E = k d Q / (r2 + d2)3/2

    Disc of rad R, d on axis: E = 2 k Q / R2 [ 1 - d / (√(R2 + d2)]

Ф = ∮ E dA = Qenc / εo    (Gauss’s Law)

k = 9 x 10^9 N m^2 / C^2   = 1 / 4 π εo  (Coulomb constant)

εo = 8.854 x 10-12 F/m   (electric permittivity constant)

Moving Charge generates a magnetic field!

B = Magnetic Field: (unit: 1 Tesla = 1 T = 1 N/Am = 1 Weber/m2 = 10,000 Gauss)

  Straight Current:  B = μI / 2πs RHR:  thumb current, fingers mag field

  Loop:   B = μI / 2r RHR:  fingers current, thumb mag field

  Coil:  B = μNI / L RHR:  fingers current, thumb mag field

F = Magnetic Force:

  Charge moving in B:  F = qvB sin θ RHR:  fingers v, curl B, thumb F

  On current:   F = ILB sin θ RHR:  fingers I, curl B, thumb F

  Between 2 currents:     F/ L =  μ I1 I2­ / 2πs    Dir:  opposite dir currents repel

  Torque on current in loop: τ = w I L B sin θ / 2    RHR:  fingers I, curl B, thumb τ

Induction: 

   Wire moving in B: V = B L v sin θ

   Mag moving in coil: V = - N Δ B A / Δt 

   Transformers: N1 / N2 = V1 / V2 = I2 / I1

    Self Induction: V = - L Δ I / Δt     where for a coil, inductance =  L = μ N2 I / ｌ

    Add inductors like resistors

    Energy stored in an inductor = E = ½ L I2

    Current thru inductor = I = Imax (1 - e-t/τ)    where τ = L / R

 μ=1.257x10^-6 Tm/A OR μ=4πx10^-7 Tm/A  (magnetic permeability constant)

C2 = 1 / εo μo 

Light: v = f λ

Reflection: θi = θr 

Refraction: n1 sin θ1 = n2 sin θ2  where  n = c / v

Internal Reflection: θCritical = sin -1 (n2 / n1) 

Apparent Depth: app depth / actual depth = h' / h = n2 / n1 

Lenses/Mirrors: 1 / di  + 1 / do  = 1 / f   and   m = hi / ho = - di / do  

Signs: + / -

f: converge / diverge      

di: real / virtual      

m: upright / inverted