Capacitors have a maximum voltage, called the working voltage or rated voltage, which specifies the maximum potential difference that can be applied safely across the terminals. Exceeding the rated voltage causes the dielectric material between the capacitor plates to break down, resulting in permanent damage to the capacitor.
The rated voltage depends on the material and thickness of the dielectric, the spacing between the plates, and design factors like insulation margins. Manufacturers determine the voltage rating through accelerated aging tests to ensure the capacitor will operate reliably below specified voltages and temperatures.
For an ideal capacitor, leakage resistance would be infinite and ESR would be zero. Unlike resistors, capacitors do not have maximum power dissipation ratings. Instead, they have maximum voltage ratings. The breakdown strength of the dielectric will set an upper limit on how large of a voltage may be placed across a capacitor before it is damaged.
When working with a capacitor, you will typically see two values printed on the side. The first is the capacitance, obviously, and the second is a voltage. This is the “breakdown voltage,” and it is the maximum voltage that the manufacturer guarantees will not damage the capacitor. You might ask yourself, “How can a voltage damage this capacitor?”
The maximum energy (U) a capacitor can store can be calculated as a function of U d, the dielectric strength per distance, as well as capacitor’s voltage (V) at its breakdown limit (the maximum voltage before the dielectric ionizes and no longer operates as an insulator):
The other use of the term "breakdown" in electronics is for breakdown voltages in diodes. For capacitors in series, 1/C [total] = 1/C + 1/C + 1/C +... For caps in parrallel, C [total] = C + C + C + ... The current and v0ltage are related by i = C (dV/dt), which are just derived from the equation Q=CV.