**Waves.** The wave speed , – the wavelength, – the frequency.

**Wave functions and wave dynamics.** The displacement of individual particles in the medium

(or, more intuitively, )

, where and

Wave function:

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# Month: September 2016

## Mechanical Waves

## Alternating Current

## Distances in the Universe

## Mutual Inductance

## Mechanical and Electrical Oscillations

## Oscillation of a Mass-Spring System Compared with Electrical Oscillation in an *L-C* Circuit

### Mass-Spring System

### Inductor-Capacitor Circuit

## Electromagnetic Induction

## General Relativity in Brief

Random notes

**Waves.** The wave speed , – the wavelength, – the frequency.

**Wave functions and wave dynamics.** The displacement of individual particles in the medium

(or, more intuitively, )

, where and

Wave function:

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**Voltage, current, and phase angle.** In general, the instantaneous voltage between two points in an ac circuit is not in phase with the instantaneous current passing through those points.

**Resistance and reactance.** The voltage across a resistor is in phase with the current, . The voltage across an inductor leads the the current by , , inductive reactance . The voltage across a capacitor lags the the current by , , capacitive reactance .

**Impedance and the L-R-C series circuit. **In general ac circuit, the voltage and current amplitutes are related by the circuit impedance , . In an

**Power in ac circuits.** The average power input to an ac circuit: , where is the phase angle of the voltage relative to the current. The factor is called the power factor of the circuit.

**Resonance angular frequencey.** .

**Transformers.** , .

P.S. Interactive “The Scale of the Universe”:

**Mutual inductance.** When a changing current in one circuit causes a changing magnetic flux in a second circuit, an emf is induced in the second circuit. and , – mutual inductance, – number of turns of coil of the first circuit, – average magnetic flux through each turn of coil 1.

**Self-inductance.** A changing current in any circuit causes a self-induced emf , – depends on the geometry of the circuit and the material surrounding it.

**Magnetic field energy.** An inductor with inductance carrying current has energy associated with the inductor’s magnetic field: . Magnetic energy density: .

**R-L**** circuits.** In an R-L circuit the growth and decay of current are exponential with time constant .

**L-C**** circuits.** An L-C circuit undergoes electrical oscillations with an angular frequency .

**L-R-C**** circuits.** The frequency of damped oscillations .

- Kinetic energy =
- Potential energy =

- Magnetic energy =
- Electrical energy =

**Faraday’s law.**Induced emf in a closed loop , – magnetic flux through the loop.**Lenz’s law.**An induced current or emf always tends to oppose or cancel out the change that caused it.**Motional emf.**.**Induced electric fields.**When an emf is induced by a changing magnetic flux through a stationary conductor, there is an induced nonconservative electric field : .**Displacement current.**A time-varying electric electric field generates displacement current , which acts as a source of magnetic field in exactly the same way as conduction current: .**Maxwell’s equations.**The relationships between electric and magnetic fields and their sources:

(Gauss’s law for fields)

(Gauss’s law for fields)

(Faraday’s law)

(Ampere’s law including displacement current).

Spacetime tells matter how to move; matter tells spacetime how to curve.

John Archibald Wheeler, from here.