hey guys, let's get started the circuit princlple, now that the mooc of this is all-text-in-english, I will take notes in English, sorry for my bad English :(

Notice: This post is closed bcuz my bad English and a demand of Chinese reading. You can find the Chinese version in here

# Base in Mathematics

In fact I’ve learned some of calculus, but none of linear algebra, also my physical is bullshit. So here is.

## Calculus

### Some relationships

The displacement:

And derivative of displacement is:

Then derivative of velocity is:

the acceleration.
Obviously,

$C$ is an arbitrary constant.

### Questions

1.The acceleration of the object is $a=\sin t \ m/s^{2}$ when $t∈(0,\pi)$, suppose the initial velocity of the object and the initial displacement of the object are both 0, find the displacement $s(\pi)$.

## Linear algebra

### Linear function

A function f(x) satisfy the following equation is a linear function. (homogeneity and additivity)

### Cramer’s rule

for

we have a matrix:

equals to it.
And we have:

### Characteristic root

The Characteristic root is$\begin{vmatrix} \lambda I -A \end{vmatrix}=0$ , for 2x2 matrix, $I = \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix}$, so we have:

so $\lambda{1}=-2$ , $\lambda{2} = -3$ , and

# Circuits in Senior Physics

Physical Quantity Symbol Unit Unit Symbol Formula
Electromotive force $E$ Volt $V$ $E=U+Ir，E=I（R+r）$
Internal resistance $r$ Ohm $\Omega$ $E=U+Ir$
Resistance $R$ Ohm $\Omega$ $R=\rho\dfrac{\ L}{S}=\dfrac{U}{I}$
Capacitance $C$ Farad $F$ $C=\dfrac{q}{U}$
Inductance $L$ Henry $H$
Electric charge $q$ Coulomb $C$ $q=It$
Current $I$ Ampere $A$ $I=neSv$
Voltage $U$ Volt $V$ $U=IR$
Electric power $P$ Watt $W$ $P=UI$
Thermal power $P$ Watt $W$ $P=I^{2}R$

# Branch Variables

## Current(电流)

Time variance rate of charges.

Unit(ampere)

Type:

• Direct Current ($dc$) <= Alternating Current ($ac$)
• Alternating Current ($I$) <= Sinusoidal ac current($i(t)$)

## Voltage(电压)

The work provided by electric filed force while moveing unit positive charge.

## Potential(电位)

The voltage form some point to the reference point, the potential of the reference point is ZERO.

Symbol: $\phi$ ($U$)

Unit: $V$(Volt)

The voltage between two points = the difference of the potential of these two points.

Drop of potential => Vlotage => Drop of voltage.((VoltageChan)电 压 酱)

## Electromotive force

The work provided by non-electric field force while moving unit positive charge.

Unit: V(Volt)

$e{BA}$, increase of potential. $e{BA}=\phi{A}-\phi{B}$

$\mu{AB}$, decrease of potential. $\mu{AB}=\phi{A}-\phi{B}$

## Capital&Small Letter

• Capital for constant variables, $U,I$.
• Small for changeable variables, $u,i$.

# Reference Direction

Associated and Non-associated

## For currents

$i>0$ when its reference direction equals to real direction.

Two ways for representing reference direction of currents

• Arrow
• Double subscript$i_{AB}$:reference direction from A to B

## For voltages

$U>0$ when its reference direction equals to real direction.

Three ways for representing reference direction of voltages:

• Arrow
• Positive and negative
• Double subscript ($U_{AB}$)

For electromotive force, $e_{BA}$ means the increase of potential from B to A.

## For power

For $p_{a} = ui$ , means element absorbs power.

• assoc.
• $P_{a}>0$% (element is really absorbing power)
• $P_{a}<0$ (element is really delivering power)

For $p_{d} = ui$ , means element delivers power.

• non-assoc.
• $P_{d}>0$ (element is really delivering power)
• $P_{d}<0$ (element is really delivering power)

Memo 1:

$p=ui$,

for assoc, it means abosorbing.

for non-assoc, it means delivering.

## For Resistor

Resistors always absorb power, regardless of the reference direction.