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11TH GRADE · OSCILLATIONS AND WAVES

Electromagnetic vibrations and alternating current

Oscillatory circuit, reactance and transformer.

32 minutes25 theory cards
Open interactive lesson

LESSON MATERIAL

Basic Concepts

3

Oscillatory circuit

A circuit of a capacitor and a coil in which electromagnetic oscillations occur.

Energy periodically transfers from the electric field of the capacitor to the magnetic field of the coil and back.

AC current

Electric current that periodically changes magnitude and direction.

For sinusoidal current, the effective values are usually used: they give the same thermal effect as the corresponding direct current.

Transformer

A device for changing alternating voltage using electromagnetic induction.

The transformer only works when the magnetic flux is changing; in an ideal model, a gain in voltage is accompanied by a decrease in current.

LESSON MATERIAL

Physical quantities

13

Capacitor charge

qq

Instant charge of the capacitor plate.

Unit: pendant · Kl\mathrm{Kl}

Charge amplitude

qmq_m

The largest modulus of charge of the capacitor.

Unit: pendant · Kl\mathrm{Kl}

Current amplitude

ImI_m

The largest current module in the circuit.

Unit: ampere · A\mathrm{A}

Inductive reactance

XLX_L

Coil resistance to alternating current.

Unit: ohm · Om\mathrm{Om}

Capacitance

XCX_C

Resistance of a capacitor to alternating current.

Unit: ohm · Om\mathrm{Om}

Voltage amplitude

UmU_m

The largest module of alternating voltage.

Unit: volt · V\mathrm{V}

EMF amplitude

Emax⁡\mathcal{E}_{\max}

The largest module of the variable EMF.

Unit: volt · V\mathrm{V}

Primary voltage

U1U_1

Voltage on the input winding of the transformer.

Unit: volt · V\mathrm{V}

Secondary voltage

U2U_2

Voltage on the output winding of the transformer.

Unit: volt · V\mathrm{V}

Primary current

I1I_1

Current strength in the input winding of the transformer.

Unit: ampere · A\mathrm{A}

Secondary current

I2I_2

Current strength in the output winding of the transformer.

Unit: ampere · A\mathrm{A}

Number of turns of the primary winding

n1n_1

The number of turns in the input winding of the transformer.

Unit: dimensionless quantity

Number of turns of the secondary winding

n2n_2

The number of turns in the output winding of the transformer.

Unit: dimensionless quantity

LESSON MATERIAL

Lesson formulas

9

Thomson's formula

T=2πLCT=2\pi\sqrt{LC}

The period of natural oscillations of the circuit is determined by inductance and capacitance.

Charge fluctuation

q=qmsin⁡(ωt+φ0)q=q_m\sin(\omega t+\varphi_0)

The charge of the capacitor changes harmoniously with the phase.

Current amplitude in the circuit

Im=qmωI_m=q_m\omega

The amplitude of the current is equal to the amplitude of the charge multiplied by the cyclic frequency.

Inductive reactance

XL=2πνLX_L=2\pi\nu L

Inductive reactance increases with frequency and inductance.

Capacitance

XC=12πνCX_C=\frac{1}{2\pi\nu C}

Capacitance decreases with increasing frequency and capacitance.

Unit of reactance

[XL]=[XC]=1 Om[X_L]=[X_C]=1\,\mathrm{Om}

Inductive and capacitive reactance are measured in ohms.

Energy of the oscillatory circuit

W0=qm22C=CUm22=LIm22W_0=\frac{q_m^2}{2C}=\frac{CU_m^2}{2}=\frac{LI_m^2}{2}

The total energy of the circuit is transferred between the electric field of the capacitor and the magnetic field of the coil.

Transformation ratio

U1U2=n1n2\frac{U_1}{U_2}=\frac{n_1}{n_2}

The voltage ratio of an ideal transformer is equal to the ratio of the number of turns.

Ideal transformer currents

U1U2=I2I1\frac{U_1}{U_2}=\frac{I_2}{I_1}

In an ideal transformer, an increase in voltage is accompanied by a decrease in current.

DIRECTORY

Related formulas

AmplitudeA, xₘ · m

PRACTICE

Tasks on the topic

Oscillations and waves11 class · 30 problems