When trying to compare the energy in a battery to the energy in a capacitor, the units don't match up. How can one compare a battery whose Ah are 10 and Voltage is 3 (for a total of 30 Wh) to a capacitor whose Farads is X and voltage is Y?
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To begin, let's call things with their names (no offense). What is measured in Farads is capacitance $C$. What is measured in $Ah$ is the charge that can be stored in a battery or a capacitor. From the definition of capacitance, the charge on the walls of a capacitor with capacitance $C$ and potential difference $V$ is $$ q = CV $$ so you obtain the value you're interested in. However, if $C$ is in Farad and $V$ is in volts, $q$ will be measured in Coulombs. $$ \text{Ampere} = \frac{\text{Coulomb}}{\text{Second}} $$ so $$ 1\text{ Ampere}\cdot\text{hour} = \text{1 Coulomb}\cdot\frac{\text{hour}}{\text{second}} = 3600 \text{ Coulombs}$$ So, in your notation, the stored charge is $XY/3600$. |
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Energy in a capacitor is $CV^2/2 = QV/2$ because its voltage starts at 0 when uncharged (unlike a battery, where the voltage is more or less constant). See note 8 in the Maxwell doc you referenced, which uses this formula and then converts from joules to watt-hours in the same fashion correctly described by Bzazz's answer. |
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