Synthetic **Summary of Physics 12 Chapter 3** the best, most complete to help you consolidate knowledge and review better.

## General Theory of Alternating Current

**I) Alternating Current:**

** – Concept:** is a current whose magnitude is a function of the sine or cosine of time.

i = I_{} cos(ωt + )

**– Characteristic quantities:**

i : instantaneous current.

I_{}: maximum amperage.

ω: angular frequency w = 2π/T = 2πf

ωt + : oscillation phase of i

φ: initial phase of i

I = I_{}/√2 : effective amperage. Meaning: if the alternating current is replaced, the maximum amperage is I_{} with a constant current, for the effect of these two currents to be the same (same capacity), the direct current must have a magnitude of I.

When calculating, measuring, … the quantities of the AC circuit, people mainly calculate or measure the r.m.s. values.

**II) Principle of generating alternating current.**

** Rule: **based on electromagnetic induction. When a wire frame with N turns of wire, area S, rotates around its axis with angular speed ω, in a uniform magnetic field B →, with a direction perpendicular to the axis of rotation. At the initial time the angle between B → and the normal vector n → of the wireframe plane is

At time t, the magnetic flux through the coil:

= NBScosα = NBS cos(ωt + )

Then in the circuit appears an induced electromotive force:

If the closed coil has a resistance R, the induced current in the circuit is:

This is alternating current.

### Theory AC circuits contain only one element

If the alternating current in the circuit is of the form i = I_{}cos(ωt)

Then the alternating voltage between the two ends of the circuit has the form u = U_{}cos(ωt + )

φ is the phase difference between u and i:

→ u,i have the same angular frequency, just go find the relationship between amplitude and phase difference φ.

Comparison table of electrical circuits containing different elements

### Circuit theory with R, L, C connected in series

**I) Ohm’s law for series R, L, and C circuits**

* Consider a circuit consisting of a resistor R, a pure inductor L and a capacitor C connected in series.

Assume the AC current in the circuit is: i = I√2 cos(ωt)

Then the voltage between the two ends of the resistor, inductor and capacitor respectively is:

u_{CHEAP }= IR√2 cos(ωt)

u_{OFFER} = IZ_{OFFER}√2 cos(ωt + /2)

u_{OLD} = IZ_{OLD}√2 cos(ωt – /2)

→ The potential difference between the two ends of the circuit is: u = u_{CHEAP} + u_{OFFER} + u_{OLD} (first)

Use the Fre-nen diagram method to replace the algebraic sum of the a.c. quantities with the corresponding rotation vector summation.

Then equation (1) becomes

(shown as figure)

is called the impedance of the circuit.

**II) Phase difference between voltage and current.**

From the figure we have: tanφ = (U_{OFFER} – U_{OLD})/U_{CHEAP} = (Z_{OFFER} – Z_{OLD})/cheap

Where is the phase difference of u with i: =_{u} –_{i}

If Z_{OFFER} > Z_{OLD} : u phase earlier than i by an angle

If Z_{OFFER} C : u lags behind i by an angle φ

**III) Resonance phenomenon.**

When Z_{OFFER} = Z_{OLD }ωL = 1/ω_{OLD} ↔ Ω^{2}OFFER_{OLD} = 1

then tanφ = 0 so

That is the phenomenon of electrical resonance.

### Theory Power consumption of AC circuit. Power factor

**I) Power of the AC circuit.**

* Consider an AC circuit with instantaneous voltage between the two ends of the circuit and the alternating current in the circuit respectively:

u = U√2cos(ωt)

i = I√2cos(ωt + )

– **Instant power** of the circuit is p = ui = 2UIcos(ωt) cos(ωt + )

= UI[cosφ + cos(2ωt + φ)]

– **Medium output** in one cycle T is:

in 1 BILLION

– If using time t >> T, then P is also the average power consumption of the circuit in time t: P = UIcosφ

**II) Power factor**

– where cos is called the power factor (because – /2

– Meaning cosφ: represents the ratio between the ability to supply electrical power to the circuit (UI) and the actual electrical power consumed in the circuit

– From the vector diagram of the RLC circuit connected in series, we have:

– Comment: So power is only consumed on R but not on L and C.

– Transform the formula for calculating power:

– Then the power consumed by the circuit in time t is: W = Pt

### Theory of Transformer Power Transmission

**I) Power loss when transmitting power.**

Electricity is transmitted from the generating plant to the consumer by a line with resistance r.

Assume the generating capacity at the plant is P_{play} = U_{play}Icosφ_{play}

Then the power loss on the line is P_{hp} = I^{2}r

Due to the series connection, the output current is also equal to the current on the wire

Comment: To reduce the power loss on the line, we can

+ Reduce

replacing copper with better conductive materials such as silver, superconducting materials, etc. → expensive. Increase wire area → increase copper volume, increase electricity pole → cost.

+ Increase the voltage at the transmitter: when U_{play} increase 10 times, then P_{hp} 100 times reduction → efficient, inexpensive → need a voltage converter.

Power transmission efficiency:

**II) Transformer:**

– Definition: A transformer is a machine that can convert alternating voltage.

– Symbol: as shown in the figure.

– Classification:

+) Booster: the machine increases the AC voltage.

+) Pressure reducing machine: the machine reduces the AC voltage.

Structure: 2 main parts:

+) Transformer core: a wrought iron frame with a silicon phase that helps to transmit all the magnetic flux from one coil to the other.

+) Two coils EASY_{first},D_{2} wound on two opposite sides of the frame, with small resistance and high inductance, with the number of turns of wire respectively N_{first},Women_{2}. The coil connected to the power source is called the primary coil, the coil connected to the consumer base is called the secondary coil.

– **Working principle:** based on electromagnetic induction.

When applying an a.c. voltage with r.m.s. value U_{first} at the beginning of the primary winding there is N_{first} turns, producing an alternating current of r.m.s. value I_{first} . Thanks to the transformer core, the flux in each turn of the primary winding is always equal to the flux in each turn of the secondary winding is equal to Ф. Since the current is alternating, the flux produced by it also varies harmonically with the same frequency. Therefore, in the secondary coil, there will be a secondary voltage with an effective value of U ._{2} and has a current of r.m.s. value I_{2}.

– Application: metal melting, electric welding, used in power transmission. In the power plant, it is necessary to use a booster to increase the voltage before generating to reduce the loss on the line.

– Experience proves:

If the transformer is ideal (no power loss P_{first} = P_{2})

### Theory of Alternators

**I) Single phase AC generator.**

– Concept: is a machine that generates a sinusoidal alternating electromotive force.

– Structure: inductor: magnets

Armature: coils connected together.

The part that rotates is called the rotor, the part that is stationary is called the stator.

Working principle: based on electromagnetic induction. The inductor with p magnets (p pairs of poles) produces a magnetic flux through the armature (wireframe). When one of the two parts rotates with speed n (revolutions/s), the magnetic flux through the armature will be biased with frequency f = pn, so in the armature there will be a sinusoidal a.c. emf of the same frequency f. .

**II) Three-phase AC generator.**

– Concept: is a machine that generates three sinusoidal alternating currents of the same frequency, same amplitude and 2π/3 phase difference.

– Structure: Three identical cylindrical coils are fixed on a circle at 3 symmetrical positions.

A male foot rotates about the axis O with a constant angular speed

– Principle of operation: similar to a single-phase AC generator. When the magnet rotates, the flux of each coil will be biased with angular frequency , the same amplitude, but 2π/3 out of phase (because the three coils are placed in 3 symmetrical positions (3 axes of the 3 coils). concurrent at O and deviated by 2π/3)

– Application: generating three-phase alternating current: is a system of 3 sinusoidal alternating currents with the same frequency, but 2π/3 phase difference, if the load is symmetrical, the 3 currents have the same amplitude.

Advantages of three-phase current: transmission of electricity over long distances, saving wires, supplying power for three-phase electromechanical devices, commonly used in factories and factories.

### Theory of three-phase asynchronous motor

**I) Asynchronous motor.**

– Rotating magnetic field: is a magnetic field with magnetic induction vectors B rotating in space. For example, when a magnet rotates around an axis, a rotating magnetic field is created.

Synchronous rotation: two objects rotate with the same angular speed. For example: place the test magnet between the two poles of a U-magnet rotating uniformly with angular speed , the test magnet will also rotate uniformly with angular speed ω

Asynchronous rotation: two objects rotate at different speeds.

For example: placing a closed wire frame between the two poles of a U-magnet rotating uniformly with angular speed ω around the axis ∆, the wireframe can also rotate around this axis. When the magnet rotates through the bias wire frame, an electric current is induced in the wire frame (the phenomenon of electromagnetic induction). then the magnetic force will apply a torque torque on the wire frame, causing the wire frame to rotate faster and chase the magnetic field. However, when the speed of the wire frame increases, the rate of flux variation decreases, the current in the wire frame decreases, and the torque torque decreases again and again until the magnetic force torque is equal to the resistance torque, the frame The wire will rotate uniformly with an angular speed less than the angular speed of the magnet.

Asynchronous motor: A motor that works on the principle of asynchronous rotation.

**II) Three-phase asynchronous motor**

– Concept: is a motor that uses three-phase current to create asynchronous rotation.

– Structure:

The stator: is a division that generates a rotating magnetic field: consists of three identical coils placed in 3 symmetrical positions on a circle.

Rotor: is a wire frame that can rotate under the action of a rotating magnetic field placed inside the stator (to increase efficiency, we combine many rotating coaxial wire frames called iron cage rotors)

– Working principle: When giving 3-phase alternating current, frequency ω passes through 3 windings of the stator, at the center O of the circle there will be a rotating magnetic field with frequency ωB equal to frequency ω. Then the rotating magnetic field will cause the rotor to rotate with an angular speed ‘ which is always less than .

or = B > ‘

Posted by: Trinh Hoai Duc High School

Category: Grade 12, Physics 12

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