Capacitance — 考前速记

核心公式

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

$\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} \quad \text{(series)}$

$C = C_1 + C_2 \quad \text{(parallel)}$

$W = \frac{1}{2} QV = \frac{1}{2} CV^2 = \frac{1}{2} \frac{Q^2}{C}$

$\tau = RC$

$I = I_0 e^{-t/RC}, \quad Q = Q_0 e^{-t/RC}, \quad V = V_0 e^{-t/RC}$

RC 放电数值关系

$t$	$x/x_0$
0	1.00
$RC$	0.37
$0.693RC$	0.50
$2RC$	0.14
$3RC$	0.050
$5RC$	0.0067

考前 checklist

• 电容定义：$C = Q/V$（charge per unit potential difference）
• 串联：$\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}$（与电阻相反）
• 并联：$C = C_1 + C_2$
• 放电公式：$x = x_0 e^{-t/RC}$（指数衰减）
• 充电公式：$x = x_0 (1 - e^{-t/RC})$
• 时间常数：$\tau = RC$（单位：s）
• 储能：$W = \frac{1}{2} QV = \frac{1}{2} CV^2$
• $t = RC$ 时剩下 37%
• $I_0 = V_0 / R$

关键句

Capacitance = charge per unit potential difference (charge on one plate / p.d. across plates).

For discharge through a resistor: $x = x_0 e^{-t/RC}$.

Energy stored in a charged capacitor: $\frac{1}{2} CV^2$.