DC Electric current and circuits

基本概念

Electrical potential difference – Voltage 电势差 – 电压

Resistivity 电阻率

$$ \rho=\frac{1}{ne\mu_e} $$

• $n$: free electrons per unit volume
• $\mu_e$: electron mobility

Capacitance

$$ C=\varepsilon\frac{A}{D} $$

其中$\varepsilon=\varepsilon_0\varepsilon_r$

$$ C=\frac{Q}{\Delta V} $$

Units-farad(F)

Mechanical load Torque

$$ \tau_m=k_m\Phi I $$

• $mechanical\ load \approx 0\Rightarrow V_R\approx 0 \Rightarrow \tau\rightarrow0$
• $mechanical\ load \approx \infty \Rightarrow V_R\rightarrow V_s\Rightarrow \tau \rightarrow k_m\Phi \frac{V_s}{R}$

Magnetic moment (magnetic dipole moment)

基本定律

Ohm’s Law

$$ V=IR $$

Kirchhoff‘s rules

• KCL (Junction Rule)

$$ \sum V_{rise} – \sum V_{drop}=0 $$

$$ \Rightarrow \sum_{loop} V_i=0 $$

• KVL：电能守恒

两种电路

Serial resistance

Total EMF: $E^{tot} = E_1+E_2+\cdots$

Parallel resistance

Summary

电流激发磁场的几种情况：

• 通电螺线管
  $$B=n\mu_0 I$$
• 通电直导线
  $$ B=\frac{\mu_0 I}{2\pi L} $$
• 带电圆环
  $$ B=\frac{\mu_0 I}{2\pi R}$$
• 带电平行圆盘之间
  $$ B=\frac{\mu_0 I_1I_2 A}{2\pi d}$$

基本粒子及射线

粒子

Electron has smaller mass than proton.

electron

• 电量：$-1.6\times10^{-19}C$
• 质量：$9.11\times10^{-31}kg$

射线

x rays

• 粒子：electron
• 频率范围：

Thermodynamics

基本概念

Fahrenheit & Degree Centigrade

$$T_K(K) = T_C(^{\degree}C)+273.15$$

Latent Heat – changing phase

$$Q=mL$$
Where $L$ is the SPECIFIC LATENT HEAT.
$L – (J/kg)$
$m – (kg)$

Heat Capacity

$$ Q=mc\Delta T$$
Where $c$ is the SPECIFIC HEAT CAPACITY.

Thermal Conductance & Resistance

Heat Capacity

$$C = \lim_{\Delta T\rightarrow0}\frac{\Delta Q}{\Delta T}$$

• At constant pressure
  $$C_p=\frac{\delta Q}{dT}$$

Molar Heat Capacity

$$c_m=\frac{C}{n}$$

$$\Rightarrow c_m=\frac{Q}{n\Delta T}$$

Internal energy

For the ideal gases:
$$U=\frac{3}{2}nRT$$

附录

附录2：DC Electric current and circuits

Resistivity

Kirchhoff‘s rules

热力学