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Test your basic knowledge |
GRE Physics
Start Test
Study First
Subjects
:
gre
,
science
,
physics
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Source-free RC Circuit
W_A < W_I
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
N²/Z (m_elec/m_red)
2. Bohr Model: Energy
Z²/n² (m_red/m_elec)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? = 1.22?/D
Ct²-x²-y²-z²
3. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
T^2 = k R^3 - k=constant
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
I = I_cm + md²
4. Perpendicular axis theorem
F = mv²/r
I_z = I_x + I_y (think hoop symmetry)
P +1/2 ? v² + ?gh = Constant
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into
5. Doppler Shift for light
C_eq = (? 1/C_i)^-1
? = ?0 root((1-v/c)/(1+v/c))
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
J = ? Fdt
6. De Broglie wavelength
E = Z²*E1
? = h/p
<T> = -<V>/2
F = -2*m(? x r)
7. Lensmaker Equation - Thin Lens
E = Z²*E1
Infinitely close to equilibrium at all times
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ0 I / 2R
8. First law of thermodynamics (explain direction of energy for each term)
F = qv×B
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = ?0 root((1-v/c)/(1+v/c))
qvb = mv²/R
9. Springs in series/parallel
? exp(-e/t)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
? = 5/3
10. Lab: Standard Deviation of Poisson
T = I?²/2
L = T - V dL/dq = d/dt dL/dqdot
ds² = (c*dt)² - ?(x_i)²
v(mean)
11. EM: Maxwell'S equations
ma + kx = 0
µ = m_e/2
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
J = E s - s = Conductivity - E = Electric field
12. Effective Potential
V(r) + L²2/2mr²
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = I_cm + (1/2)m d^2
Asin(?) = m?
13. Source Free RL Circuit
Opposing charge induced upon conductor
Cos[?] Sin[?] -Sin[?] Cos[?]
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
14. Work (P - V)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P1V1 - P2V2 / (? - 1)
µ = m_e/2
PdV +dU
15. Triplet/singlet states: symmetry and net spin
S_mean = s/Sqrt[N]
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = qv×B
16. Law of Mass Action
E = Z²*E1
qvb = mv²/R
? = 1.22?/D
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
17. Polarizers - intensity when crossed at ?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
P² ~ R³
I = I_0 Cos[?]^2
18. Self Inductance
Exp(N(µ-e)/t)
u dm/dt
V = -L di/dt
? exp(-e/t)
19. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
Const: 2t = (n +.5)? Destructive 2t = n?
F = -2*m(? x r)
Z_c = -i/(?C) ; Z_L = i ? L
20. Angular momentum operators L^2 and L_z
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I = I_0 Cos[?]^2
dU = 0 ? dS = ?dW/T
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
21. Expectation value of the energy of state |?>
NC?T
E = <?| H |?>
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
? = h/p
22. Lab: Accuracy of Measurements
Measurements close to true value
? = 1.22?/D
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Dp/dt = L / (t ?V)
23. Resonance frequency of LC circuit
T^2 = k R^3 - k=constant
1/vLC
F_f = µ*F_N
qvb = mv²/R
24. Pauli matrices
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
E = <?| H |?>
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
X_L = i?L
25. Force on a wire in magnetic field
C_eq = (? 1/C_i)^-1
F = I L X B
S = k ln[O] ; dS = dQ/T
?= h/v(2mE)
26. Helmholtz Free Energy
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
U - ts = -tlog(Z)
W_A < W_I
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
27. Stefan-Boltzmann law for blackbodies (power per area and T)
L = mr²d?/dt
0
P/A = s T^4
? (t-vx/c²)
28. EM: AC Resonance
(3/2) n R ?t
A[B -C] + [A -C]B
µ=s^2
X_L = X_C or X_total = 0
29. Work done on a gas
DW = P dV
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = mv²/r
M? = 2dsin(?)
30. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
V(r) + L²2/2mr²
? = ?0 root((1-v/c)/(1+v/c))
31. EM: Electromagnetic inertia
F = qv×B
<?|O|?>
Faraday/Lenz: current inducted opposes the changing field
T = I?²/2
32. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
NC?T
L = T - V dL/dq = d/dt dL/dqdot
I = V/R exp(-t/RC)
33. Invariant Energy Quantity
µ0 I / 2R
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
E²-p²c²
34. Magnetic Dipole Moment and Torque
Z = ?g_i*exp(-E/kT)
µ = Current * Area T = µ x B
F = f* (c+v_r)/(c+v_s)
T = I?²/2
35. Commutator identities ( [B -A C] - [A -B] )
S_mean = s/Sqrt[N]
?_max = b/T
F = f* (c+v_r)/(c+v_s)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
36. Quant: Expectation Value
Braking Radiation
Sin(?) = ?/d
V = -L di/dt
<?|O|?>
37. Atom: Positronium Reduced Mass
µ = m_e/2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Z²/n² (m_red/m_elec)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
38. Energy in Inductor
?~T
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
.5 LI²
E = Z²*E1
39. SR: Spacetime Interval
F = -2*m(? x r)
F = mv²/r
ds² = (c*dt)² - ?(x_i)²
v(mean)
40. Planck Radiation Law
F_f = µ*F_N
F = -2*m(? x r)
µ=s^2
Hbar*?³/(p²c³exp(hbar?/t)-1)
41. Thermo: Adiabatic Work vs Isothermal Work
(° of Freedom)kT/2
Asin(?) = m?
W_A < W_I
?= h/v(2mE)
42. Solid: Resistivity of Semi-Conductor
?~1/T
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?_max = b/T
Exponentially decreasing radial function
43. Thermo: Average Total Energy
0
.5 LI²
(° of Freedom)kT/2
F = µ0 q v I / 2pr
44. Magnetic Field For Current in Long Wire
µ0 I / 2pR
L = L_0 Sqrt[1-v^2/c^2]
PdV +dU
Hbar*?³/(p²c³exp(hbar?/t)-1)
45. Delta Function Potential - type of WF
?_max = b/T
F = qv×B
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Asin(?) = m?
46. Perturbations
I = Im (sinc²(a)) ; a = pai sin(?) / ?
H = H_0 + ?H
Opposing charge induced upon conductor
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
47. Mech: Impulse
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
1/2 CV²
Braking Radiation
J = ? Fdt
48. Relativistic Energy
?mc²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I ' = I cos²(?)
49. Kepler'S Three Laws
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
X_L = i?L
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
50. Doppler shift for light
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
PdV +dU
(3/2) n R ?t