Halliday Physics Chapter 26 · 평생 소원이 누룽지

1. Electric Current

Electric Current: 단면을 통과하는 알짜 전하의 이동률 $i = \dfrac{\mathrm dq}{\mathrm dt} \quad [\text{A = C/s}]$

Current Density($J$): 단위 면적당 전류 $J = \dfrac{I}{A}$
비균일한 경우 $I = \iint \mathbf{J} \cdot \mathrm d \mathbf{A} = \iint J \cos \theta\ \mathrm dA$
Drift Speed: $J = nev_{\text{d}}$, $I = Aev_{\text{d}}n$

Resistance: 저항값
$R = \dfrac{V}{I} \quad \text{[$\Omega$ = V/A]}$
Resistivity & Conductivity
- Resistivity: $\rho = \dfrac{E}{J} \quad [\Omega \cdot \text{m}]$
- Conductivity: $\sigma = \dfrac{1}{\rho} = \dfrac{J}{E}$

$V = EL \Rightarrow E = \dfrac{V}{L}$, $J = \dfrac{i}{A}$

$\rho = \dfrac{E}{J} = \dfrac{VA}{Li} = R \left( \dfrac{A}{L} \right) \Rightarrow V = iR$

Ohm's Law: $J = \sigma E$, $E = \rho J$
Ohmic Device & Non-Ohmic Device
- Ohmic Device: $V = iR$ 성립
- Non-Ohmic Device: $V = iR$ 성립 X(ex: 반도체)

$F = eE = ma \Rightarrow a = \dfrac{eE}{m}$

$v_{\text{d}} = a \tau = \left( \dfrac{eE}{m} \right) \tau$ ($\tau$: 충돌 사이 평균 시간)

$J = ne \left( \dfrac{eE}{m} \tau \right) = \left( \dfrac{ne^2 \tau}{m} \right) E = \sigma E$

Therefore $\rho = \dfrac{1}{\sigma} = \dfrac{m}{ne^2 \tau} = \text{const.} \Rightarrow$ Ohm's Law 성립

$\mathrm dU = \mathrm dq \cdot V \Rightarrow P = \dfrac{\mathrm dU}{\mathrm dt} = \dfrac{\mathrm dq}{\mathrm dt} V = iV \quad \text{[W = J/s]}$

Resistor에서 열에너지 손실(Joule Heating)

$V = iR$ 대입 $\Rightarrow P = i^2 R = \dfrac{V^2}{R}$

Temperature Coefficient of Resistivity($\alpha$): $\rho - \rho_0 = \rho_0 \alpha (T - T_0)$
금속에서, $T$ ↑ $\Rightarrow$ $\tau$ ↓ $\Rightarrow$ $\rho$ ↑ ($\alpha > 0$)
반도체에서, $T$ ↑ $\Rightarrow$ $n$ ↑ $\Rightarrow$ $\rho$ ↓ ($\alpha < 0$)
초전도체: 임계온도 $T_{\text{c}}$ 이하로 냉각되면 $\rho = 0$