Energy Stored on a Capacitor

电容器上的储能

The energy stored on a capacitor can be calculated from the equivalent expressions:

电容器中储存的能量可以通过等效表达式计算：

This energy is stored in the electric field.

这种能量储存在电场中。

From the definition of voltage as the energy per unit charge, one might expect that the energy stored on this ideal capacitor would be just QV. That is, all the work done on the charge in moving it from one plate to the other would appear as energy stored. But in fact, the expression above shows that just half of that work appears as energy stored in the capacitor. For a finite resistance, one can show that half of the energy supplied by the battery for the charging of the capacitor is dissipated as heat in the resistor, regardless of the size of the resistor.

根据电压定义为单位电荷的能量，人们可能会期望理想电容器上储存的能量就是QV。也就是说，将电荷从一个极板移动到另一个极板所做的所有功都会转化为能量储存。但实际上，上面的表达式表明，只有其中一半的功会储存在电容器中。对于有限的电阻，可以证明，电池为电容器充电所供给的能量中，无论电阻大小，一半会以热的形式在电阻中损耗。

Electric Field Energy in Capacitor

电场能量在电容器中

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The energy stored on a capacitor is in the form of energy density in an electric field is given by

电容器中储存的能量以电场中的能量密度形式存在，其表达式为

This can be shown to be consistent with the energy stored in a charged parallel plate capacitor

这可以证明与带电平行板电容器中储存的能量一致