Physical knowledge points: 1. Motion of particle (1)- linear motion.

1) moving in a straight line at a uniform speed

1. average speed Vping = s/t (definition) 2. Useful inference VT2-VO2 = 2as.

3. Intermediate speed vt/2 = Vping = (vt+VO)/2 4. Final speed vt = VO+AT.

5. Intermediate position speed vs/2 = [(VO2+VT2)/2] 1/26. Displacement S = V level T = VOT+AT2/2 = vt/2t.

7. Acceleration A =(vt-Vo)/t {With Vo as the positive direction, A and Vo are in the same direction (accelerating) a>0; On the other hand, a < 0}

8. It is inferred experimentally that δs = at2 {δs is the displacement difference of continuous adjacent equal time (t)}

9. Main physical quantity and unit: initial velocity (VO): m/s; Acceleration (a): m/s2; Terminal speed (vt): m/s; Time (t) seconds (s); Displacement (s): m; Distance: meters; Speed unit conversion:1m/s = 3.6km/h.

note:

(1) The average speed is a vector;

(2) When the speed of the object is high, the acceleration is not necessarily high;

(3)a=(Vt-Vo)/t is only a measure, not a judgment;

(4) Other related contents: particle, displacement and distance, reference system, time and moment [see Volume I P 19]/S-T diagram, V-T diagram/speed and speed, instantaneous speed [see Volume I P24].

2) Free falling body movement

1. Initial velocity VO = 0 2. Final speed VT = GT.

3. Falling height H = GT2/2 (calculated downward from Vo position) 4. Inference Vt2=2gh.

note:

(1) Free falling body is a uniformly accelerated linear motion with zero initial velocity, which follows the law of uniformly variable linear motion.

(2) A = G = 9.8m/S2 ≈ 10m/S2 (the gravity acceleration near the equator is small, and the mountain is smaller than the flat, and the direction is vertical downward).

(3) Vertical throwing.

1. Displacement S = VOT-GT2/22. The final speed vt = VO-gt (g = 9.8m /S2 ≈10m/S2).

3. Useful inference VT2-VO2 =-2G4. Maximum lifting height hm = VO2/2g (from the throwing point)

5. Round trip time t = 2vo/g (time from throwing back to original position)

note:

(1) Full-course treatment: it is a linear motion with uniform deceleration, with positive upward direction and negative acceleration;

(2) subsection treatment: the upward movement is a straight line movement with uniform deceleration, and the downward movement is a free fall, which is symmetrical;

(3) The process of ascending and descending is symmetrical, for example, at the same point, the speed is equal and the direction is opposite.

Second, the motion of particles (2)-curve motion, gravity

1) flat throwing motion

1. Horizontal speed: VX = VO 2. Vertical speed: vy = GT.

3. horizontal displacement: x = vot4. Vertical displacement: y = gt2/2.

5. Exercise time t = (2 y/g) 1/2 (usually expressed as (2h/g) 1/2)

6. Closing speed vt = (vx2+vy2)1/2 = [VO2+(gt) 2]1/2.

The angle β between the closing speed direction and the horizontal plane: tgβ = vy/VX = gt/v0.

7. Joint displacement: s = (x2+y2) 1/2,

Angle α between displacement direction and horizontal plane: tgα = y/x = gt/2vo.

8. Horizontal acceleration: ax = 0；; Vertical acceleration: ay = g

note:

(1) Flat throwing motion is a curvilinear motion with uniform change, and the acceleration is g, which can usually be regarded as the synthesis of uniform linear motion in horizontal direction and free falling motion in vertical direction;

(2) The movement time is determined by the falling height h(y) and has nothing to do with the horizontal throwing speed;

(3) The relationship between θ and β is TGβ= 2tgα；; ;

(4) The time t of flat throwing is the key to solving the problem; (5) An object moving along a curve must have acceleration. When the direction of velocity and the direction of resultant force (acceleration) are not in a straight line, the object moves in a curve.

2) Uniform circular motion

1. linear velocity v = s/t = 2π r/t 2. Angular velocity ω = φ/t = 2π/t = 2π f.

3. centripetal acceleration a = v2/r = ω 2r = (2π/t) 2R4. Centripetal force f center = mv2/r = mω 2r = mr (2π/t) 2 = mω v = f.

5. Period and frequency: t = 1/f 6. Relationship between angular velocity and linear velocity: v = ω r.

7. The relationship between angular velocity and rotational speed ω = 2 π n (frequency and rotational speed have the same meaning here).

8. Main physical quantities and units: arc length (s): meter (m); Angle (φ): radian (rad); Frequency (f): Hertz; Period (t): seconds (s); Rotational speed (n): rpm; Radius (r): meter (m); Linear speed (v): m/s; Angular velocity (ω): radians per second; Centripetal acceleration: m/s2.

note:

(1) The centripetal force can be provided by a specific force, resultant force or component force, and the direction is always perpendicular to the speed direction and points to the center of the circle;

(2) The centripetal force of an object moving in a uniform circular motion is equal to the resultant force, and the centripetal force only changes the direction of the speed, not the size of the speed, so the kinetic energy of the object is unchanged, and the centripetal force does not do work, but the momentum is constantly changing.

3) Gravity

1. Kepler's third law: t2/r3 = k (= 4π 2/gm) {r: orbital radius, t: period, k: constant (independent of the mass of the planet, depending on the mass of the central celestial body)}.

2. Law of gravitation: f = GM1m2/R2 (g = 6.67×10-1n? M2/kg2, the direction is on their connection)

3. Gravity and gravity acceleration on celestial bodies: GMM/R2 = mg; G = GM/R2 {R: celestial radius (m), m: celestial mass (kg)}

4. Orbital velocity, angular velocity and period of the satellite: v = (GM/R)1/2; ω=(GM/R3) 1/2； T = 2π (R3/GM) 1/2 {m: mass of central celestial body}

5. The first (second and third) cosmic velocity V 1 = (G and r)1/2 = (GM/r)1/2 = 7.9 km/s; V2 = 1 1.2km/s； V3 =16.7km/s

6. Geosynchronous satellite GMM/(R+H) 2 = M4 π 2 (R+H)/T2 {H ≈ 36,000 km, H: height from the earth's surface, R: radius of the earth}

note:

(1) The centripetal force required for celestial motion is provided by gravity, and the F direction = F million;

(2) The mass density of celestial bodies can be estimated by applying the law of universal gravitation.

(3) Geosynchronous satellites can only run over the equator, and the running period is the same as the earth's rotation period;

(4) When the orbit radius of the satellite decreases, the potential energy decreases, the kinetic energy increases, the speed increases and the period decreases.

(5) The maximum circling speed and minimum launching speed of the Earth satellite are 7.9 km/s. ..

III. Force (common force, composition and decomposition of force)

1) ordinary force

1. Gravity G = mg (vertical downward direction, G = 9.8m/S2 ≈ 10m/S2, the point of action is at the center of gravity, which is applicable to the vicinity of the earth's surface).

Hooke's law f = kx {direction is along the direction of recovery deformation, k: stiffness coefficient (N/m), x: deformation variable (m)}

3. Sliding friction force f =μFN {opposite to the relative motion direction of the object, μ: friction coefficient, FN: positive pressure (n)}

4. Static friction force 0≤f Static ≤fm (contrary to the relative motion trend of objects, fm is the maximum static friction force)

5. Gravity F = GM1m2/R2 (g = 6.67×10-11n? M2/kg2, the direction is on their connection)

6. Electrostatic force F = kq1Q2/R2 (k = 9.0×109N? M2/C2, the direction is on their connecting line)

7. electric field force f = eq (e: field strength N/C, q: electric quantity c, the electric field force applied to the positive charge is in the same direction as the field strength).

8. Ampere force f = bilsin θ (θ is the angle between b and l, when L⊥B: f = Bil, when B//L: f = 0).

9. Lorentz force f = qvbin θ (θ is the included angle between B and V, when V⊥B: f = qvb, when V//B: f = 0).

note:

(1) The stiffness coefficient k is determined by the spring itself;

(2) The friction coefficient μ has nothing to do with pressure and contact area, but is determined by the material characteristics and surface conditions of the contact surface.

(3)fm is slightly larger than μFN, which is generally considered as FM ≈ μ fn;

(4) Other related contents: static friction (magnitude and direction) [see P8]; In the first volume];

(5) Symbol and unit of physical quantity B: magnetic induction intensity (T), L: effective length (M), I: current intensity (A), V: charged particle velocity (m/s), Q: charged particle (charged body) electric quantity (C);

(6) The directions of Ampere force and Lorentz force are determined by the left-hand rule.

2) Composition and decomposition of force

1. The resultant force on the same straight line has the same direction: f = f 1+F2, and the opposite direction: f = f 1-F2 (f 1 > F2).

2. Composition of mutually angled forces:

When f = (f12+f22+2f1f2cos α)1/2 (cosine theorem) f1⊥ F2: f = (f12+f22)/kloc.

3. resultant force range: | f1-F2 |≤ f≤| f1+F2 |

4. Orthogonal decomposition of force: FX = FCOS β, FY = FSIN β (β is the included angle between the resultant force and the X axis TG β = FY/FX).

note:

The synthesis and decomposition of (1) force (vector) follow the parallelogram law;

(2) The relationship between resultant force and components is equivalent substitution, and resultant force can be used to replace the * * * interaction of components, and vice versa;

(3) In addition to the formula method, it can also be solved by drawing method. At this time, we must choose the scale and draw strictly;

(4) When the values of F 1 and F2 are constant, the greater the included angle (α angle) of F 1 and F2, the smaller the resultant force;

(5) The combination of forces on the same straight line can be taken along the positive direction of the straight line, and the direction of forces is represented by symbols, which is simplified as algebraic operation.

Four. Dynamics (motion and force)

1. Newton's First Law of Motion (Law of Inertia): An object has inertia and always maintains a uniform linear motion state or a static state until an external force forces it to change this state.

2. Newton's second law of motion: f = ma or a = f/ma (determined by external force and consistent with the direction of external force)

3. Newton's third law of motion: f =-F' (the negative sign indicates that the directions are opposite, and f and f' interact, and the balance force is different from the reaction force. Practical application: recoil movement).

4. The balance f of * * * point force is equal to 0, which summarizes the {orthogonal decomposition method and the intersection principle of three forces}.

5. Overweight: FN>g, weightlessness: fn

6. Applicable conditions of Newton's law of motion: it is suitable for solving low-speed motion problems, for macroscopic objects, for dealing with high-speed problems, and for microscopic particles [see Volume I, P67].

Note: the equilibrium state means that the object is at rest or moving in a straight line at a uniform speed, or rotating at a uniform speed.

Verb (abbreviation of verb) vibration and wave (mechanical vibration and propagation of mechanical vibration)

1. Simple harmonic vibration f =-kx {f: restoring force, k: proportional coefficient, x: displacement, and the negative sign indicates that the direction of f is always opposite to x}

2. The period of a simple pendulum t = 2π (l/g) 1/2 {l: pendulum length (m), g: local gravity acceleration value, provided that the pendulum angle θ.

3. Forced vibration frequency characteristics: F = F driving force

4. Conditions for occurrence of * * * vibration: F driving force = F solid, A = Max * * * Prevention and application of vibration [see Volume I, P 175].

5. Mechanical waves, shear waves and longitudinal waves [see P2 Volume II]

6. Wave velocity v = s/t =λf =λ/t {In the process of wave propagation, one period propagates forward by one wavelength; The wave velocity is determined by the medium itself.

7. Sound wave velocity (in air) 0℃; 332 m/s; 20℃； 344 m/s; 30℃； 349 m/s; (Sound waves are longitudinal waves)

8. Conditions for obvious diffraction of waves (waves continue to propagate around obstacles or holes): the size of obstacles or holes is less than the wavelength, or there is little difference.

9. Interference conditions of waves: the two waves have the same frequency (constant phase difference, similar amplitude and the same vibration direction).

10. Doppler effect: Due to the mutual movement between the wave source and the observer, the transmitting frequency of the wave source is different from the receiving frequency (the receiving frequency increases when they are close to each other, and decreases when they are opposite [see Volume II P2 1]].

note:

(1) The natural frequency of an object has nothing to do with amplitude and driving force frequency, but depends on the vibration system itself;

(2) The strengthened area is the place where the peaks meet or the valleys meet, and the weakened area is the place where the peaks meet;

(3) The wave only propagates vibration, and the medium itself does not migrate with the wave, which is a way to transfer energy;

(4) Interference and diffraction are Porter's;

(5) Vibration image and fluctuation image;

(6) Other related contents: ultrasonic wave and its application [see Volume II P22]/ Energy transformation in vibration [see Volume I p 173].

Impulse and momentum of intransitive verbs (the change of force and momentum of an object)

1. momentum: p = mv {p: momentum (kg/s), m: mass (kg), v: speed (m/s), which is in the same direction as speed}

3.Impulse: I = ft {I: Impulse (n？ S), f: constant force (n), t: action time of force (s), and the direction is determined by f}

4. Momentum theorem: I = Δ P or FT = MVT–MVO {Δ P: momentum change Δ δP = MVT-MVO, which is a vector type}

5. Law of conservation of momentum: p = p after the total or p'' can also be m1v1+m2v2 = m1v1'+m2v2'

6. Elastic collision: δ p = 0; Ek = 0 (i.e. conservation of momentum and kinetic energy of the system)

7. Inelastic collision δ p = 0; 0 & ltEK & ltδ EKm {δ ek: kinetic energy loss, EKm: maximum kinetic energy loss}

8. Completely inelastic collision δ p = 0; Δ δek =δekm {connected into a whole after contact}

9. The object m 1 collides with the stationary object m2 elastically at the initial velocity of v 1;

v 1′=(m 1-m2)v 1/(m 1+m2)v2′= 2m 1v 1/(m 1+m2)

10. Inferred from 9-the exchange speed (kinetic energy conservation, momentum conservation) between them in elastic collision of equal mass.

1 1. The mechanical energy loss when the horizontal velocity vo of the bullet M shoots at the long wooden block M resting on the horizontal smooth ground and is embedded in it to move together.

E loss = mvo2/2-(m+m) vt2/2 = fs relative to {vt:* * * * same speed, f: resistance, s relative to the displacement of the bullet relative to the long block}

Seven, work and energy (work is a measure of energy conversion)

1. work: w = fscos α (definition) {w: work (j), f: constant force (n), s: displacement (m), α: angle between f and s}

2. Gravity work: WAB = mghab {m: mass of the object, g = 9.8m/S2 ≈ 10m/S2, hab: height difference between A and B (hab = ha-HB)}

3. Work done by electric field force: WAB = QUAB {Q: electric quantity (C), UAB: potential difference between A and B (V), that is, UAB = φ A-φ B}

4. Electric power: w = UIT (universal) {U: voltage (V), I: current (A), T: power-on time (S)}

5. power: p = w/t (definition) {p: power [w], w: work done in time (j), t: time spent doing work (s)}

6. Automobile traction power: p = FvP level = Fv level {P: instantaneous power, P: average power}

7. The car starts at constant power and constant acceleration, and the maximum running speed of the car (VMAX = P /f)

8. Electric power: P = UI (universal) {U: circuit voltage (V), I: circuit current (A)}

9. Joule's Law: q = i2rt {q: electrothermal (j), i: current intensity (a), r: resistance value (Ω), t: electrifying time (s)}

10. I = u/r in pure resistance circuit; p = UI = U2/R = I2R； Q=W=UIt=U2t/R=I2Rt

1 1. kinetic energy: ek = mv2/2 {ek: kinetic energy (j), m: m/s)} object (kg), v: instantaneous velocity of object (m/s)}

12. gravitational potential energy: EP = mgh {EP: gravitational potential energy (j), g: gravitational acceleration, h: vertical height (m) (from zero potential energy surface)}

13. potential: ea = q φ a {ea: point a charged body potential (j), q: electric quantity (c), φ a: point a potential (v) (from zero potential plane)}

14. kinetic energy theorem (positive work is done on an object, and the kinetic energy of the object increases);

W = mvt2/2-mvo2/2 or w = δ ek.

{W = total work done by external force on an object, Δ ek: kinetic energy change Δ ek = (MVT2/2-MVO2/2)}

15. conservation law of mechanical energy: δe = 0 or EK 1+EP 1 = EK2+EP2, or mv12+mgh1= mv22/2+mgh2.

16. Variation of gravitational work and gravitational potential energy (gravitational work is equal to the negative value of the increment of gravitational potential energy of an object) WG =-δ EP.

Eight, molecular dynamics theory, law of conservation of energy

1.Avon gadro constant na = 6.02×1023/mol; The molecular diameter is in the order of 10- 10 meter.

2. Measurement of molecular diameter by oil film method D = V/s {V: single molecule oil film volume (m3), S: oil film surface area (m) 2}

3. Content of molecular dynamics theory: Matter is composed of a large number of molecules; A large number of molecules do random thermal motion; There are interactions between molecules.

4. Intermolecular attraction and repulsion (1) r

(2) r = r0, f citation = f repulsion, f molecular force = 0, and e molecular potential energy = =Emin (minimum value).

(3)r & gt； R0，f quote >； F repulsion and f molecular force represent gravity.

(4)r & gt； 10r0, f = F repulsion ≈0, f molecular force ≈0, e molecular potential energy ≈0.

5. The first law of thermodynamics w+q = Δ u {(work and heat transfer, two ways to change the internal energy of an object, the effect is equivalent),

W: the positive work done by the outside world on the object (J), Q: the heat absorbed by the object (J), and δ U: the increased internal energy (J), which involves that the perpetual motion machine of the first kind cannot be built (see Volume II P40).

6. The second law of thermodynamics

Kirkhner's statement: it is impossible to transfer heat from a low-temperature object to a high-temperature object without causing other changes (directionality of heat conduction);

Kelvin's statement: it is impossible to absorb heat from a single heat source and use it all to do work without causing other changes (directionality of mechanical energy and internal energy transformation) {it involves that the second type of perpetual motion machine cannot be built [see Volume II P44]}.

7. The third law of thermodynamics: thermodynamic zero cannot be reached (lower limit temperature of the universe: -273. 15 degrees Celsius (thermodynamic zero)).

note:

(1) Brownian particles are not molecules. The smaller the Brownian particle, the more obvious Brownian motion, and the higher the temperature, the more intense Brownian motion.

(2) Temperature is a sign of average kinetic energy of molecules;

3) The intermolecular attraction and repulsion exist at the same time, and decrease with the increase of intermolecular distance, but the repulsion decreases faster than the attraction;

(4) When the molecular force does positive work, the molecular potential energy decreases, and at r0, F attraction = F repulsion, and the molecular potential energy is the smallest;

(5) The gas expands, and the outside world does negative work on the gas W.

(6) The internal energy of an object refers to the sum of all kinetic energy of molecules and molecular potential energy of an object. For an ideal gas, the intermolecular force is zero and the molecular potential energy is zero;

(7)r0 is the distance between molecules at molecular equilibrium;

(8) Other related contents: energy transformation and invariance law [see p 4 1]/ energy development and utilization, environmental protection [see P47]/ internal energy, kinetic energy of molecules and molecular potential energy [see p 47].

Nine, the nature of gas

1. State parameters of gas:

Temperature: macroscopically, the degree of heat and cold of an object; Microscopically, it is a sign of the irregular motion intensity of molecules inside an object.

Relationship between thermodynamic temperature and celsius temperature: t = t+273 {t: thermodynamic temperature (k), t: celsius temperature (℃)}

Volume V: the space occupied by gas molecules, and the unit is1m3 =103l =106ml.

Pressure P: In unit area, a large number of gas molecules frequently collide with the impactor wall, resulting in continuous and uniform pressure. The standard atmospheric pressure is1ATM =1.013x105pa = 76cmhg (1pa =1n/m2).

2. Characteristics of gas molecular movement: large intermolecular gap; Except the collision moment, the interaction force is weak; The molecular motion rate is very high.

3. Equation of state of ideal gas: p1v1/t1= p2v2/t2 {PV/t = constant, t is thermodynamic temperature (K)}

note:

(1) The internal energy of an ideal gas has nothing to do with the volume of the ideal gas, but is related to the temperature and the amount of substances;

(2) The conditions for the establishment of Equation 3 are all ideal gases with a certain mass. When using the formula, we should pay attention to the unit of temperature, where t is the temperature in degrees Celsius (℃) and t is the thermodynamic temperature (k).

Electric field

1. Two kinds of charges, law of charge conservation and elementary charge: (e =1.60×10-19c); The charge of a charged body is equal to an integer multiple of elementary charge.

2. Coulomb's law: f = kq 1q2/r2 (in vacuum) {f: the force between point charges (n), k: the electrostatic constant k = 9.0× 109N? M2/C2, Q 1, Q2: the electric quantity of two charges (c), R: the distance between two charges (m), the direction is on their connecting line, the acting force and reaction force repel each other, and the different charges attract each other.

3. Electric field intensity: e = f/q (definition formula, calculation formula) {e: electric field intensity (N/C), which is a vector (electric field superposition principle), and q: the quantity of electric charge (c).

4. The electric field formed by the vacuum point (source) charge E = kq/R2 {R: the distance from the source charge to this position (m), Q: the electric quantity of the source charge}

5. The field strength of uniform electric field E = UAB/D {Voltage between two points in the field strength direction (V)UAB:AB and the distance between two points (M)}

6. Electric field force: f = QE {f: electric field force (n/c)}, q: electric quantity of charge affected by electric field force (c), e: electric field strength (N/C)}

7. Potential and potential difference: UAB =φa-φb, UAB = WAB/Q =-δ EAB/Q.

8. Work done by electric field force: WAB = Kwab = EQD {WAB: Work done by electric field force when charged body goes from A to B (J), Q: Charged amount (C), UAB: potential difference (V) between points A and B in electric field (the work done by electric field force has nothing to do with the path), E: uniform electric field strength, and D: along the field strength direction.

9. Electric potential energy: ea = q φ a {ea: electric potential energy (j) of charged body at point A, q: electric quantity (c), φ a: potential at point A (v}.

10. Variation of electric potential energy δEAB = e B-EA {difference of electric potential energy when charged body moves from position A to position B in electric field}

1 1. The change of electric field force work and electric potential energy δ eab =-wab =-quab (the increment of electric potential energy is equal to the negative value of electric field force work)

12. capacitance c = q/u (definition formula, calculation formula) {c: capacitance (f), q: electric quantity (c), u: voltage (potential difference between two plates) (v)}

13. The capacitance of parallel plate capacitor C = ε s/4 π KD (S: the area opposite to two plates, D: the vertical distance between two plates, ω: the dielectric constant).

Ordinary capacitance [see Volume II, P 1 1 1]

14. acceleration of charged particles in electric field (VO = 0):w =δek Δ ek or qu = mvt2/2, vt = (2qu/m) 1/2.

15. Deflection when charged particles enter a uniform electric field at a speed Vo in a direction perpendicular to the electric field (regardless of gravity)

Quasi-flat vertical electric field direction: uniform linear motion L = VOT (in parallel plates with E=U/d heterogeneous charges: E = U/D)

Throwing motion is parallel to the direction of electric field: uniformly accelerating linear motion with zero initial velocity D = AT2/2 and A = F/M = QE/M.

note:

(1) When two identical charged metal balls are in contact, the power distribution law is that different kinds of original charges are neutralized first and then evenly divided, and the total amount of the same kind of original charges is evenly divided;

(2) The electric field line starts with positive charge and ends with negative charge. The electric field lines do not intersect, and the tangent direction is the field strength direction. The electric field is strong where the electric field lines are dense, and the potential along the electric field lines is getting lower and lower, and the electric field lines are perpendicular to the equipotential lines;

(3) memorize the electric field line distribution requirements of common electric fields (see Figure [Volume II P98]);

(4) The electric field strength (vector) and electric potential (scalar) are determined by the electric field itself, and the electric field force and electric potential are also related to the electric quantity and the positive and negative charges of the charged body;

(5) In electrostatic balance, the conductor is an equipotential body with an equipotential surface, the electric field line near the outer surface of the conductor is perpendicular to the surface of the conductor, the synthetic field strength inside the conductor is zero, there is no net charge inside the conductor, and the net charge is only distributed on the outer surface of the conductor;

(6) Capacitance unit conversion:1f =106μ f =1012pf;

(7) Electron Volt (eV) is the unit of energy,1EV =1.60×10-19j;

(8) Other related contents: electrostatic shielding [see Volume II P101]/oscilloscope and its application [see Volume II P14] equipotential surface [see Volume II P 105].

XI。 constant current

1. current intensity: i = q/t {i: current intensity (a), q: the amount of electricity passing through the lateral load surface of the conductor in time t (c), t: time (s)}

2. ohm's law: I = u/r {I: conductor current intensity (a), u: voltage across the conductor (v), r: conductor resistance (ω)}

3. Resistance, resistance law: r = ρ l/s {ρ: resistivity (ω? M), l: the length of the conductor (m), s: the cross-sectional area of the conductor (m2)

4. Ohm's Law of Closed Circuit: I = E/(R+R) or E = IR+IR can also be E = U inside +U outside.

{I: total current in the circuit (A), E: electromotive force of power supply (V), R: external circuit resistance (ω), R: internal resistance of power supply (ω)}

5. Electric power and power: W = UIT, P = UI {W: electric power (J), U: voltage (V), I: current (A), T: time (S), P: electric power (W)}

6. Joule's Law: q = i2rt {q: electrothermal (j), i: current passing through conductor (a), r: resistance value of conductor (ω), t: electrifying time (s)}

7. In a pure resistance circuit, because I = u/r and W = q, W = Q = UIT = I2RT = U2T/R.

8. Total power activity, power output and power efficiency: pTotal = IE, pOutput = IU, η = ptout/ptotal {i: total circuit current (a), e: power electromotive force (v), u: terminal voltage (v), η: power efficiency}.

9. Series/parallel series circuit of the circuit (P, U is proportional to R) Parallel circuit (P, I is inversely proportional to R)

Resistance relation (series-same-parallel-opposite) r series = r1+R2+R3+1/rparallel =1/r1+/R3+

The current relation I is always = I1= I2 = i3 and = i 1+I2+i3+

The voltage relationship utotal = u1+U2+u3+utotal = u1= U2 = u3.

Power distribution Ptotal = p1+P2+P3+Ptotal = p1+P2+P3+

10. Measure the resistance with an ohmmeter.

(1) circuit composition (2) measurement principle

After the two probes are short-circuited, adjust Ro to make the instrument pointer full of bias, and obtain

Ig=E/(r+Rg+Ro)

After connecting the measured resistor Rx, the current through the meter is

Ix = e/(r+rg+ro +Rx) = e/(r+rx)

Because Ix corresponds to Rx, it can represent the measured resistance.

(3) Usage: mechanical zero adjustment, range selection, ohm zero adjustment, measurement reading (pay attention to gear (amplification)) and gear off.

(4) Note: When measuring the resistance, disconnect it from the original circuit, select the measuring range so that the pointer is near the center, and re-short the ohm to zero in each gear.

1 1. Voltammetry to measure resistance.

Internal connection of ammeter: external connection of ammeter:

Voltage representation: U = UR+UA current representation: I = IR+IV.

Measured value of Rx = u/I = (ua+ur)/IR = ra+rx > measured value of r = u/I = ur/(IR+iv) = rvrx/(RV+r).

Select circuit condition Rx>& gtRA[ or Rx & gt(RARV) 1/2] circuit condition rx.

12. Current-limiting wiring and voltage-dividing wiring of sliding rheostat in circuit

Small voltage regulating range, simple circuit, low power consumption, large voltage regulating range, complex circuit and high power consumption.

Selection conditions of voltage regulation RP >; Rx is convenient to adjust the selection conditions of voltage RP.

Twelve. magnetic field

1. Magnetic induction intensity is a physical quantity used to express the strength and direction of magnetic field, and it is a vector. The unit is (t), 1t = 1n/a? m

2. Ampere force f = BIL；; (Note: L⊥B) {B: magnetic induction intensity (T), F: ampere force (F), I: current intensity (A), L: wire length (m)}

3. Lorentz force f = qvb (note v ⊥ b); M/s)} Spectrometer [see Volume II, P 155] {F: Lorentz Force (N), Q: Charged Particle Electricity (C), V: Charged Particle Velocity (m/s)}

4. In the case of ignoring gravity (regardless of gravity), the movement of charged particles into the magnetic field (master two kinds):

(1) charged particles enter the magnetic field along the direction of parallel magnetic field: they move in a straight line at a uniform speed without Lorentz force v = v0.

(2) Charged particles enter the magnetic field along the direction perpendicular to the magnetic field: make uniform circular motion, and the law is as follows: (a)F direction = FLUO = MV2/R = mω 2r = Mr (2π/t) 2 = qvb; r = mV/qB； t = 2πm/qB； (b) The period of motion has nothing to do with the radius and linear velocity of circular motion, and Lorentz force does no work on charged particles (anyway); (c) Key to solving the problem: draw the trajectory, find the center of the circle, and determine the angle between the radius and the center of the circle (= twice the tangent angle).

Thirteen, electromagnetic induction

1.[ Calculation formula of induced electromotive force]

1) e = n Δ φ/Δ t (universal formula) {Faraday's law of electromagnetic induction, e: induced electromotive force (V), n: number of turns of induction coil, Δ φ/Δ t: magnetic flux change rate}

2) E = BLV vertical (cutting magnetic induction line movement) {L: effective length (m)}

3) EM = NBS ω (maximum induced electromotive force of alternator) {EM: peak value of induced electromotive force}

4) E = BL2Ω/2 (one end of the conductor is fixed and cut by Ω) {Ω: angular velocity (rad/s), v: speed (m/s)}

2. magnetic flux φ = bs {φ: magnetic flux (Wb), b: magnetic induction intensity of uniform magnetic field (t), s: facing area (m2)}

3. The positive and negative poles of induced electromotive force can be determined by the direction of induced current (current direction inside the power supply: from negative pole to positive pole).

*4. Self-induced electromotive force Efrom = nΔ φ/Δ t = lΔ i/Δ t {l: self-inductance coefficient (h) (the coil with iron core is larger than the coil without iron core), Δ i: changing current,? T: time taken, δ I/δ T: change rate (change speed) of self-induced current}

Note: (1) The direction of induced current can be determined by Lenz's law or right-hand rule, and the application points of Lenz's law [see Volume II, P173]; (2) Self-induced current always hinders the change of current that causes self-induced electromotive force; (3) Unit conversion:1h =103mh =106μ h (4) Other related contents: self-inductance [see Volume II p 178]/ fluorescent lamp [see Volume II p 180].

XIV. Alternating current (sinusoidal alternating current)

1. Instantaneous value of voltage E = EMSINΩ t Instantaneous value of current I = IMSINΩ t; (ω=2πf)

2. EMF peak value EM = NBS ω = 2 BLV current peak value (in pure resistance circuit) IM = EM/R total

3. Effective value of sine (cosine) alternating current: e = em/(2)1/2; u = Um/(2) 1/2； I=Im/(2) 1/2

4. The relationship between voltage, current and power in the primary and secondary windings of an ideal transformer.

u 1/U2 = n 1/N2； I 1/I2 = N2/N2； P input = p output

5. In long-distance transmission, using high voltage to transmit electric energy can reduce the loss of electric energy on transmission lines: p loss' = (p/u) 2r; (P loss): the power lost on the transmission line, P: the total power of transmitted electric energy, U: transmission voltage, R: transmission line resistance) [see Volume II P198];

6. Physical quantities and units in formula 1, 2, 3 and 4: ω: angular frequency (rad/s); T: time (seconds); N: number of turns of the coil; B: magnetic induction intensity (t);

S: coil area (m2); U: (output) voltage (v); I: current intensity (a); P: power (w).

note:

(1) The change frequency of alternating current is the same as the rotation frequency of the coil in the generator, that is, ω electricity = ω line and F electricity = F line;

(2) In the generator, the magnetic flux of the coil is the largest at the neutral surface position, and the induced electromotive force is zero, so the direction of the current passing through the neutral surface changes;

(3) The effective value is defined according to the thermal effect of current, and the AC value without special explanation refers to the effective value;

(4) When the turns ratio of an ideal transformer is constant, the output voltage is determined by the input voltage, the input current is determined by the output current, and the input power is equal to the output power. When the power consumed by the load increases, the input power also increases, that is, P out determines P in.

(5) Other related contents: sinusoidal alternating current image [see Volume II P190]/Influence of resistance, inductance and capacitance on alternating current [see Volume II P 193].

Fifteen. Reflection and refraction of light (geometrical optics)

1. reflection law α = I {α; Reflection angle, I: incident angle}

2. Absolute refractive index (light from vacuum to medium) n = c/v = sin/sin {dispersion of light, red light in visible light has a small refractive index, n: refractive index, c: light speed in vacuum, v: light speed in medium,: incident angle,: refraction angle}.

3. Total reflection: 1) Critical angle C: SINC = 1/n when light enters vacuum or air from medium.

2) Conditions for total reflection: light dense medium is injected into light hydrophobic medium; The incident angle is equal to or greater than the critical angle.