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.


Some relationships

The displacement:

And derivative of displacement is:

Then derivative of velocity is:

the acceleration.

$C$ is an arbitrary constant.


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


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 $W$ $P=I^{2}R$


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Branch Variables


Time variance rate of charges.



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


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


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:


for assoc, it means abosorbing.

for non-assoc, it means delivering.

For Resistor

Resistors always absorb power, regardless of the reference direction.