Yes, the voltage across a capacitor can be negative, but this depends on how you define and measure it. Here’s a detailed explanation:
### Capacitor Basics
A capacitor stores electrical energy by accumulating charges on its plates. The voltage across a capacitor (\(V_C\)) is determined by the difference in electric potential between its two plates.
### Voltage Polarity
1. **Definition of Voltage**: The voltage across a capacitor is defined as the potential difference between its two terminals. If we call the voltage on one plate \(V_1\) and the voltage on the other plate \(V_2\), then the voltage across the capacitor \(V_C\) is given by:
\[
V_C = V_1 - V_2
\]
2. **Negative Voltage**: If \(V_2\) is greater than \(V_1\), then \(V_C\) will be negative. In other words, if the voltage on the positive plate is less than the voltage on the negative plate, the resulting voltage across the capacitor will be negative.
### Practical Implications
1. **AC Circuits**: In alternating current (AC) circuits, the voltage across a capacitor can swing positive and negative as the AC voltage oscillates. For example, during one half-cycle of a sinusoidal AC signal, the capacitor might experience a positive voltage, and during the other half-cycle, it might experience a negative voltage.
2. **DC Circuits**: In direct current (DC) circuits, if the capacitor is connected in a manner where the polarity of the applied voltage reverses (such as when switching polarities in a circuit), the capacitor can also experience a negative voltage.
### Important Considerations
1. **Polarity Sensitivity**: While the voltage across a capacitor can be negative, many capacitors are designed to handle only positive voltages relative to their polarity markings. Electrolytic capacitors, for example, are polarized and must be connected with the correct polarity to avoid damage. Applying a negative voltage across such capacitors (with incorrect polarity) can lead to failure, leakage, or explosion.
2. **Measurement**: When measuring the voltage across a capacitor, ensure that the polarity of the measurement probes is consistent with the definition used in your circuit or analysis. If your measurement device reads a negative value, it simply indicates that the voltage on the positive terminal is lower than the voltage on the negative terminal.
In summary, yes, the voltage across a capacitor can be negative, depending on how you define the reference points and the type of signal applied.