1, standard equation: (x-a) 2+(y-b) 2 = r 2;

2. General equation: x 2+y 2+dx +Ey+f = 0 (note: where the square of d+the square of e-4f >; 0);

oblong

(x^2/a^2)+(y^2/b^2)= 1(a>； The focus of b>0 is on the x axis; B>a>0 focuses on the Y axis);

hyperbola

(x 2/a 2)-(y 2/b 2) = 1 (focus x axis) (y 2/a 2)-(x 2/b 2) = 1 (focus y axis);

parabola

Y 2 = 2px (focus X positive) y 2 =-2px (focus X negative) x 2 = 2py (focus Y positive) x 2 =-2py (focus Y negative)

(The following content is taken from netizens)

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 {UAB voltage (V) between UAB and AB, and the distance (M) between D and AB in the field strength direction}

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].

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:

Voltage expression: u = ur+ua

External connection of ammeter:

Current expression: I = IR+IV

The measured value of Rx = u/I = (ua+ur)/IR = ra+rx > R is true.

Rx = u/I = ur/(IR+iv) = rvrx/(RV+r) measured value.

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

Select circuit condition rx

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

Current limiting connection

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

Selection conditions of voltage regulation RP >; prescription

Large voltage regulating range, complex circuit and high power consumption.

Selection conditions of voltage regulation RP

Note 1) Unit conversion:1a =103ma =106μ a; 1kV = 103v = 106ma； 1mω= 103kω= 106ω

(2) The resistivity of various materials changes with the change of temperature, and the resistivity of metals increases with the increase of temperature;

(3) The total resistance in series is greater than any partial resistance, and the total resistance in parallel is less than any partial resistance;

(4) When the power supply has internal resistance and the external circuit resistance increases, the total current decreases and the terminal voltage increases;

(5) When the external circuit resistance is equal to the power supply resistance, the output power of the power supply is maximum, and the output power is E2/(2r);

(6) Other related contents: the relationship between resistivity and temperature, semiconductors and their applications, superconductivity and their applications [see Volume II, P 127].