电容器的能量与功率

概述

Capacitors store energy in an electric field between their plates. The stored energy and the power available during discharge are fundamental to designing timing circuits, power supplies, and energy storage systems. This page covers the core formulas for energy storage, instantaneous power delivery, and discharge time under constant-power loading.

关键公式

Energy Stored in a Capacitor

$W = \frac{1}{2} C V^2$

Where W is the energy stored (joules), C is capacitance (farads), and V is the voltage across the capacitor (volts).

Average Power During Discharge

$P = \frac{W}{t} = \frac{C V^2}{2\,t}$

This gives the average power over a discharge pulse of duration t. In practice, discharge starts at a peak and decays, so this is a rough engineering estimate rather than a constant instantaneous value.

Discharge Time at Constant Power Load

$t = \frac{W}{P} = \frac{C V^2}{2\,P}$

重新整理功率方程得到将电容器完全放电到负载所需的时间ad that consumes power P at a constant rate.

变量

计算示例

A 10 µF capacitor is charged to 230 V.

Stored energy:

$W = \frac{1}{2} \times 10 \times 10^{-6} \times 230^2 = 0.265 \text{ J}$

Average power if discharged in 5 µs:

$P = \frac{0.265}{5 \times 10^{-6}} = 52\,900 \text{ W} \approx 53 \text{ kW}$

单位换算器

原始源图

以下原始来源图像予以保留，以免丢失视觉参考资料。当图像包含图表或表格数据时，其提取值已呈现在页面的表格、计算器或交互式图表中；其余图像保留为视觉来源参考。

Capacitor

Source Table Coverage

The cached source includes Engineering ToolBox layout/search rows around the calculator area. The substantive migrated content is preserved as the capacitor energy calculator, dielectric breakdown table, original capacitor image, and the unit converter above.

工程要点

• 指数衰减： 在电阻负载电路中，电压（因此瞬时功率r) decays exponentially — not linearly. The $P = W/t$ formula yields a rough average over the pulse duration, not the peak.
• 峰值功率更高： 放电开始时瞬时功率为 $P_{\text{peak}} = V^2 / R$ (for a resistive load), which can far exceed the average value.
• ESR 限制： 实际电容器具有等效串联电阻 (ESR)，限制峰值电流ent and converts some energy to heat inside the component rather than the load.
• 安全设计裕度： 始终将工作电压降额到远低于介电击穿 value, accounting for temperature, aging, and transient overvoltage.

Breakdown Voltage by Dielectric

Puncture voltage measured at 1 MHz. Values in V per mil (1 mil = 0.001 inch ≈ 25.4 µm).

This dielectric breakdown table is retained as source-related capacitor design reference material needed for completeness of the migrated capacitor page; it supports the voltage derating and safe working-voltage notes above.

Actual breakdown depends on temperature, frequency, dielectric thickness, and electrode geometry. Consult manufacturer datasheets for rated working voltages.

参考资料

• Original Source — Capacitors Energy Power