Question

Why are capacitor voltages continuous?

Answer 1

Capacitor voltages are continuous because of how a capacitor works and the nature of electric charge. Here’s a simple explanation:

A capacitor stores electric charge. When a voltage is applied across its plates, charge builds up on the plates. This process takes time, and the amount of charge stored on the plates depends on the voltage applied.

Now, for a voltage to change abruptly across the capacitor, the charge on the plates would have to change instantly. But this isn't possible in practice because of the physical properties of capacitors: the current (the flow of charge) has to change gradually. If the voltage were to change instantaneously, it would require an infinite amount of current, which is not possible.

So, the voltage across a capacitor can't change suddenly — it changes smoothly and continuously over time instead.

To summarize:
- The capacitor’s voltage is continuous because charge can’t accumulate or deplete instantly.
- The current required to change the voltage would have to be infinite, which doesn’t happen in real circuits.

This is a fundamental property of capacitors and makes sense in both DC and AC circuits, where the voltage change is smooth and gradual.