Knowledge point 1. The related concepts of fractions let A and B represent two algebraic expressions. If b contains letters, the formula is called a fraction. Note that the value of denominator b cannot be zero, otherwise the score is meaningless. A fraction with no common factor between numerator and denominator is called simplest fraction. If the numerator and denominator have common factors, they should be simplified. 2. Basic properties of fractions (m is an algebraic expression not equal to zero) 3. Scores. 4. Zero index 5. Negative Integer Exponent Note that the operation property of positive integer power can be extended to integer exponential power, that is, m and n in the above formula can be O or negative integers. 6. General steps to solve the fractional equation: multiply the simplest common denominator on both sides of the equation, remove the denominator, and become an integral equation. To solve this integral equation and check the root is to substitute the root of the integral equation into the simplest common denominator to see if the result is zero. If the result is 0, it means that this root is an additional root of the original equation and must be omitted. 7. The general steps to solve the application problem of fractional equation are: (1) check the meaning of the problem; (2) Set an unknown number (with unit); (3) List the formulas according to the quantitative relationship in the topic, find out the equal relationship and list the equations; (4) Solve the equation and check the root to see if the solution of the equation meets the meaning of the question; (5) Write the answer (there must be a unit). The first quadrant (+,+), the second quadrant (-,+), the third quadrant (-,-) and the fourth quadrant (+,-) of the proportional, inverse and linear functions; The ordinate of a point on the X axis is equal to 0; conversely, all points with the ordinate equal to 0 are on the X axis, and the abscissa of a point on the Y axis is equal to 0. On the contrary, all points with abscissa equal to 0 are on the Y axis. If a point is on the bisector of the first and third quadrants, its abscissa is equal to its ordinate; if a point is on the bisector of the second and fourth quadrants, its abscissa and ordinate are opposite to each other. If two points are symmetrical about x, the abscissa is equal and the ordinate is opposite; If two points are symmetrical about y axis, the ordinate is equal and the abscissa is opposite; If two points are symmetrical about the origin, the abscissa and ordinate are mutually opposite numbers. 1, definition of linear function and proportional function (1) If y=kx+b(k, b is constant, k≠0), then y is called a linear function of x (2) When b = 0, the linear function y=kx+b is y = kx (k) At this point, y is called the positive proportional function of X. Note: the proportional function is a special linear function, and the linear function contains the proportional function. 2. The image and properties of the proportional function (1) The image of the proportional function y=kx(k≠0) is a straight line passing through (0,0) (1,k). (2) when k >; At 0, y increases with the increase of x, and the straight line y=kx rises from left to right through the first and third quadrants. When k < 0, y decreases with the increase of x, and the straight line y = kx decreases from left to right through the second and fourth quadrants. 3. The image and properties of linear function (1) The image of linear function y=kx+b(k≠0) is a straight line passing through (0, b) (-, 0). Note: (0, b) is the coordinate of the intersection of the straight line and the Y axis, and (-,0) is the coordinate of the intersection of the straight line and the X axis. (2) when k >; At 0, y increases with the increase of x, and at k, the straight line y=kx+b(k≠0) rises; 0, b<0 straight line passes through the first, third and fourth quadrant (3) k.

First, the circuit

The formation of current: the directional movement of charge forms current.

Current direction: from the positive pole to the negative pole of the power supply.

Power supply: a device that can provide continuous current (or voltage).

Power supplies convert other forms of energy into electrical energy. For example, dry cells convert chemical energy into electrical energy. The generator converts mechanical energy into electrical energy.

Conditions for continuous current: power supply and circuit must be closed.

Conductor: Objects that are easy to conduct electricity are called conductors, such as metal, human body, earth, salt solution, etc.

Insulator: Objects that are not easy to conduct electricity are called insulators, such as glass, ceramics, plastics, oil and pure water.

Circuit composition: consists of power supply, wires, switches and electrical appliances.

The circuit has three states: (1) path: the connected circuit is called path; (2) Open circuit: A broken circuit is called an open circuit; (3) Short circuit: The circuit that directly connects the wires to the two poles of the power supply is called short circuit.

Circuit diagram: A diagram showing circuit connections with symbols is called a circuit diagram.

Series connection: connecting elements one by one in sequence is called series connection. If you disconnect anywhere, the current will disappear. )

Parallel connection: connecting elements in parallel is called parallel connection. (each branch does not affect each other. )

Second, at present

International unit: ampere (a); Commonly used: mA, microampere (A), 1 amp = 103 mA = 106 microampere.

The instrument for measuring current is ammeter, and its usage rules are as follows:

(1) ammeter should be connected in series in the circuit;

(2) Current flows from the "+"terminal and from the "-"terminal;

(3) The measuring current should not exceed the range of ammeter;

Never connect the ammeter to the two poles of the power supply without using electrical appliances.

The ammeter commonly used in the laboratory has two measuring ranges: ① 0 ~ 0.6 A, and the current represented by each battery is 0.02 A；;

② 0 ~ 3 A, and the current value represented by each unit is 0.1a. 。

Third, voltage.

Voltage (U): Voltage is the cause of current generation in the circuit, and power supply is the device that provides voltage.

International unit: Volt (V); Commonly used: KV, MV. 1kv = 103V = 106MV。

The instrument for measuring voltage is voltmeter, and the usage rules are as follows:

① The voltmeter should be connected in parallel in the circuit;

(2) Current flows from the "+"terminal and from the "-"terminal;

③ The measured voltage should not exceed the range of voltmeter;

The voltmeter commonly used in the laboratory has two measuring ranges: ① 0 ~ 3 volts, and the voltage represented by each battery is 0. 1 volt;

② 0 ~15v, and the voltage represented by each cell is 0.5v..

Memory voltage value: ① 1 the voltage of dry cell is 1.5 volts; ② The voltage of1lead battery is 2 volts; (3) household lighting voltage is 220 volts; ④ safe voltage: not higher than 36V; ⑤ The industrial voltage is 380 volts.

Fourth, resistance.

Resistance (R): indicates the resistance of the conductor to the current.

The greater the resistance of a conductor, the smaller the current passing through it.

International unit: ohm (ω); Commonly used: Megaohms (mω), Kilohms (kω); 1 megohm =103kohm; 1 kω = 103 ω。

The factors that determine the resistance are material, length, cross-sectional area and temperature (R has nothing to do with its U and I).

Sliding rheostat:

Principle: Change the resistance by changing the length of the resistance wire in the circuit.

Function: Change the current and voltage in the circuit by changing the resistance in the circuit.

Nameplate: If the sliding rheostat is marked with "50Ω", it means that the maximum resistance is 50Ω and the maximum allowable current is 2A.

Correct use: a, should be used in series in the circuit; B, wiring should be "up and down"; C, the resistance value should be adjusted to the maximum before electrifying.

Ohm's Law

Ohm's Law: The current in a conductor is directly proportional to the voltage across the conductor and inversely proportional to the resistance of the conductor.

Formula: where the unit is I→ an (a); U→ volt (v); R→ Europe (ω).

Understanding of the formula:

① I, U and R in the formula must be in the same circuit;

② If any two quantities of I, U and R are known, the other quantity can be found;

(3) the unit should be unified when calculating.

Application of ohm's law;

(1) the resistance of the same resistor is constant, regardless of current and voltage, its current increases with the increase of voltage. (R=U/I)

② When the voltage is constant, the greater the resistance, the smaller the current (I=U/R).

(3) when the current is constant, the greater the resistance, the greater the voltage across the resistance. (U=IR)

The series connection of resistors has the following characteristics: (refer to R 1, R2 is connected in series, and the more series connections, the greater the resistance).

① Current: I=I 1=I2 (the currents in all parts of the series circuit are equal).

② voltage: U=U 1+U2 (the total voltage is equal to the sum of all voltages).

③ Resistance: R=R 1+R2 (total resistance is equal to the sum of all resistances). If n equivalent resistors are connected in series, R =nR.

④ partial pressure function: =; Calculate U 1, U2, available as:

⑤ Proportional relation: current: I1:I2 =1:1(q is heat).

The parallel connection of resistors has the following characteristics: (R 1, R2 is connected in parallel, and the more parallel connections, the smaller the resistance).

① Current: I=I 1+I2 (the main current is equal to the sum of the currents of each branch).

② voltage: U=U 1=U2 (main voltage is equal to each branch voltage).

③ Resistance: (the reciprocal of the total resistance is equal to the sum of the reciprocal of each resistance) If n equivalent resistances are connected in parallel, there is RTotal = R..

④ Shunt function: I 1 is calculated, and I2 is available:

⑤ Proportional relation: voltage: U 1:U2= 1: 1, (q is heat).

Intransitive verbs electricity and electricity

1. Electric work (w): The electric energy converted into other forms of energy is called electric work.

2. International unit of work: Joule. Commonly used: degree (kWh), 1 degree = 1 kWh =3.6? 06 joules.

3. Tool for measuring power: electric energy meter

4. Electric power formula: W=Pt=UIt (where the unit is W→ Coke (J); U→ volt (v); I→an(a)； T→ seconds).

Pay attention to when calculating with W=UIt:

① W.U.I and T in the formula are in the same circuit;

(2) Units should be unified when calculating;

③ It is known that any three quantities can find the fourth quantity. There is another formula: =I2Rt.

Electric power (P): indicates the speed at which current does work. International unit: Watt (W); Commonly used unit: kW

Formula: where the unit is p → w; W→ coke; T→ seconds; U→ Volt (V), I→ An (A)

Units should be unified when using calculations.

(1) if W uses coke, T uses seconds, and the unit of P is Watt;

If w uses kWh, t uses hours, and the unit of p is kW.

10. The correct formula can also be used to calculate electric power: P=I2R, p = u2/r.

1 1. Rated voltage (U0): the normal working voltage of electrical appliances. In addition, the rated current.

12. Rated power (P0): the power of electrical appliances at rated voltage.

13. actual voltage (u): the voltage actually applied to the electrical appliance. In addition, the actual current.

14. actual power (p): the power of electrical appliances under actual voltage.

When U > U0, P > P0 is bright and easy to burn.

When u < U0, then p

When U = U0, then P = P0 emits light normally.

15. The same resistor, connected to different voltages, has; For example, when the actual voltage is half the rated voltage, the actual power is 1/4 rated power. For example, "220V 100W" is connected in the circuit of 1 10V, and the actual power is 25W. )

16. thermal power: the thermal power of a conductor is directly proportional to the square of the current and the resistance of the conductor.

17.P Thermal formula: P=I2Rt, (where the unit is p→ w); I→an(a)； R→ Europe (ω); T→ seconds. )

18. When all the work (electric work) done by current passing through a conductor is used to generate heat (electric heating), there is: thermal power = electric power, which can be calculated by electric power formula. (such as electric heaters, the resistance is like this. )

Seven. Household electricity consumption

The home circuit consists of incoming wires (live wire and neutral wire) → electric energy meter → master switch → safe → electrical appliances.

All household appliances are connected in parallel with sockets, and electrical appliances should be connected in series with their switches.

Fuse: made of lead-antimony alloy with high resistivity and low melting point. Its function is that when there is too much current in the circuit, it will heat up to the melting point and fuse, automatically cut off the circuit and play a safe role.

There are two reasons for excessive circuit current: one is short circuit; Second, the total power of electrical appliances is too large.

The principles of safe use of electricity are as follows: ① Don't touch low-voltage charged bodies; (2) don't close to the high voltage charged body.

Eight, electricity and magnetism

Magnetism: the property that an object attracts iron, nickel, cobalt and other substances.

Magnets: Magnetic objects are called magnets. It has directionality: north and south.

Magnetic pole: The strongest part of a magnet is called a magnetic pole.

Any magnet has two magnetic poles, one is the North Pole (N Pole); The other is the South Pole.

The function between magnetic poles: magnetic poles with the same name repel each other and magnetic poles with different names attract each other.

Magnetization: the process of magnetizing an object without magnetism.

There is a magnetic field around the magnet, and the interaction between magnetic poles occurs through the magnetic field.

Basic properties of magnetic field: the effect of magnetic force on magnets entering it.

Magnetic field direction: the direction of the north pole when the small magnetic needle is at rest is the magnetic field direction at this point.

Magnetic induction line: an imaginary curve describing the strength and direction of magnetic field. It doesn't exist or intersect, and it goes out in the north and enters in the south.

At a certain point in the magnetic field, the direction of the magnetic field and the direction of the magnetic induction line are the same.

10. The geomagnetic north pole is near the geographical south pole; The geomagnetic south pole is near the geographical north pole, but they do not overlap. Their intersection angle is called magnetic declination, which was first described by China scholar Shen Kuo.

1 1. Oster experiment proves that there is a magnetic field around the electrified wire.

12. Ampere's Law: Hold the solenoid with the right hand and bend it in the direction of the current in the solenoid with four points.

Then the end pointed by the thumb is the north pole (N pole) of the solenoid.

13. Characteristics of energized solenoid: ① The greater the current, the stronger the magnetism;

② The more turns of the coil, the stronger the magnetism;

(3) Inserting the soft iron core greatly enhances the magnetism.

④ The polarity of the energized solenoid can be changed by the current direction.

14. electromagnet: a solenoid with an iron core inside constitutes an electromagnet.

15. Characteristics of electromagnet:

① The presence or absence of magnetism is controlled by the on-off of current;

② The magnetic force can be adjusted by changing the current and the number of turns of the coil;

③ The current direction can change the magnetic pole.

16. electromagnetic relay: it is essentially a switch controlled by electromagnet. Its function can realize remote operation, low voltage and weak current control high voltage and strong current, and realize automatic control.

17. Basic principle of telephone: vibration → changing current → vibration.

18. electromagnetic induction: when a part of the conductor of a closed circuit cuts a magnetic induction line in a magnetic field, a current is generated in the conductor. This phenomenon is called electromagnetic induction, and the generated current is called induced current. Application: Generator.

Conditions of induced current:

① The circuit must be closed;

(2) Only a part of the conductor of the circuit is in the magnetic field;

③ This part of the conductor moves to cut the magnetic induction line.

Direction of induced current: It is related to the movement of conductor and the direction of magnetic induction line.

Generator principle: electromagnetic induction phenomenon. Structure: stator and rotor. It converts mechanical energy into electrical energy.

Influence of magnetic field on current: live wire will be acted by magnetic force in magnetic field. It is converted from electric energy to mechanical energy. Application: Motor.

The force direction of charged conductor in magnetic field is related to the direction of current and magnetic induction line.

Motor principle: it is made by using the principle that the electrified coil is forced to rotate in the magnetic field.

Commutator: realize the interchange of alternating current and direct current.

Alternating current: a current that periodically changes the direction of the current.

Direct current: current with constant direction.

experiment

1. Voltammetric resistance measurement

Experimental principle: (experimental equipment, circuit diagram is shown on the right)

Note: Before the experiment, the sliding rheostat should be adjusted to the maximum resistance.

The function of sliding rheostat in the experiment is to change the voltage across the measured resistor.

2. Measuring the electric power of small light bulbs-experimental principle: p = ui