Which of the following can damage a capacitor?

Applying too much voltage to a capacitor can lead to damage because capacitors have a specified voltage rating. This rating indicates the maximum voltage that can be applied across the capacitor without causing it to fail. When the voltage exceeds this limit, it can cause insulation breakdown within the capacitor, leading to short circuits, leakage, or even catastrophic failure. Additionally, excessive voltage can overheat the dielectric material inside the capacitor, further contributing to its deterioration and potential failure.

In contrast, other options may not necessarily result in damage under typical conditions. For example, while high frequencies can affect circuit performance, modern capacitors can be designed to function effectively at high frequencies without damage. Connecting a capacitor to a resistor is a common practice in circuits, typically used for various functions such as timing, filtering, or voltage division, and doesn't inherently harm the capacitor. Operating in a cold environment may impact performance, but it doesn't directly harm the capacitor, as many capacitors are rated for a range of temperatures and can function properly without damage at low temperatures.