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A clear formula sheet for the Science of Energy Technologies exam.
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Coulomb’s law Torque on an electric dipole Electric potential energy of two point chargesF = k ⋅ (|q1 ⋅ q2| / r2) τ = p ⋅ E in N/m U = k ⋅ (q ⋅ q0 / r)
k = 1 / (4πε0) p=q⋅d
Potential due to a point charge
Electric field Dielectrics V = U / q0 = k ⋅ (q / r)
(Force per charge) Resultant electric field
E = F / q0 E = Ơ / ε = Ơ / (K ⋅ ε0) = E0 ⋅ K Capacitance
q0 is the test charge. C = Q / Vab in Farad F.
Energy per volume
Electric field of a point charge (vacuum) Capacitance of a parallel-plate capacitor in
E = k ⋅ (q / r2) U0 = U / volume = 0.5 ⋅ ε0 ⋅ E2 vacuum
C = ε0 ⋅ A / d
Energy stored in a capacitor Other material
U = 0,5 ⋅ C ⋅ V2 = 0,5 ⋅ Q ⋅ V Udielectric = 0,5 ⋅ ε ⋅ E2 Capacitors in parallel
V1 = V2
Supercapacitor Ctot = C1 + C2 + …
C = ε ⋅ (A / d) large A and small d
Current Ohm’s law Capacitors in series
I = dQ / dt Voltage (drop) per current Vtot = V1 + V2 + …
V=I⋅R 1/Ctot = 1/C1 + 1/C2 + …
Current density
J = n ⋅ q ⋅ vd in A/m2 Resistance of a wire Equivalent capacitance
R = ρ ⋅ (l / A) ρ is the resistivity Ceq = Q / V
I=J⋅A in Ω ⋅ m. Resistors in series Kirchhoff’s rules
The ideal source of EMF Resistivity I1 = I2 Junction rule
ℰ = Vab = I ⋅ R ρ=E/J Rtot = R1 + R2 + … ΣI = 0
Power
Real sources of EMF P=I⋅V Resistors in parallel Loop rule
(Internal resistance) P = I2 ⋅ R in serial circuit Itot = I1 + I2 + … ΣV = 0
Vab = ℰ - I ⋅ r P = V2 / R in parallel circuit 1/Rtot = 1/R1 + 1/R2 + …
Transformers RC-circuits Alternating current
V2 / V1 = N2 / N1 ℰ - i(t) ⋅ R – (q(t) / C) = 0 (Sinusoidally varying current and voltage)
i = I cos 𝜔 ⋅ t I is the current amplitude and 𝜔 is the
Currents in transformers Charge capacitor angular frequency.
V1 ⋅ I1 = V2 ⋅ I2 q(t) = ℰbatt ⋅ C ⋅ (1 –
e-(1/RC)*t) Root-mean-square value
Relative energy loss i(t) = dq / dt = I0 ⋅ e-t/RC Irms = I / √2
(i ⋅ R) / P = (P ⋅ R) / V2
2
Discharge capacitor Vrms = V / √2
For a pure resistor
q(t) = Q0 ⋅ e(-1/RC)*t
Black-body radiation Pav = 0,5 ⋅ V ⋅ I
i(t) = dq / dt = I0 ⋅ e-t/RC
Ơ ⋅ T4 An equivalent expression
i(t) = dq(t) / dt
Power, we get on earth Pav = Vrms ⋅ Irms
v(t) = q(t) / C
P = π ⋅ R2 ⋅ I
U(t) = q2(t) / 2C
I is irradiance. Average power into a general AC circuit
Pav = Vrms ⋅ Irms cos ø
λmax ⋅ T = constant
Energy of a photon Quantization of angular momentum
Ephoton = h ⋅ f = (h ⋅ c)/ λ Ln = m ⋅ vn ⋅ rn = n ⋅ (h / 2π)
Electrons cross the energy gap
Photoelectric effect Radius of nth orbit in the Bohr model
when: Eph > Eg
eV0 = h ⋅ f – ø Rn = ε0 ⋅ (n2h2) / (πme2)
Total energy for nth orbit in the Bohr model
Net current across p-njunction
Momentum of a photon En = -(hcR) / n2 R is Rydberg constant
i = idiff - idrift
p=E/c=h⋅f/c=h/λ Rn = (me4) / (8ε0h3c)
i = i0 ⋅ (eeV/kT – 1)
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