How is a capacitor's charge related to its voltage?

A capacitor's charge is directly proportional to its voltage, as described by the equation Q=CV.

In more detail, the relationship between a capacitor's charge (Q) and its voltage (V) is governed by the equation Q=CV, where C is the capacitance of the capacitor. This equation is known as the capacitance equation. It states that the charge stored in a capacitor is equal to the product of its capacitance and the voltage across it.

Capacitance (C) is a measure of a capacitor's ability to store electrical charge. It is defined as the amount of charge that can be stored per unit voltage. The unit of capacitance is the farad (F), named after the English scientist Michael Faraday. One farad is equal to one coulomb per volt.

The voltage (V) across a capacitor is the electrical potential difference between its two plates. When a voltage is applied to a capacitor, it creates an electric field between the plates, causing positive charges to accumulate on one plate and negative charges on the other. This accumulation of charge is what we refer to as the capacitor's charge (Q).

The capacitance equation Q=CV shows that if you increase the voltage across a capacitor, the charge stored in the capacitor will also increase, assuming the capacitance remains constant. Conversely, if you decrease the voltage, the charge will decrease. This is because the charge is directly proportional to the voltage. To understand this relationship further, exploring the concept of electric potential energy can provide deeper insights into how energy is stored in a capacitor.

It's also worth noting that the charge-voltage relationship is linear for a capacitor, meaning that a graph of charge against voltage would be a straight line. This linearity is mirrored in concepts such as equipotential surfaces, which illustrate the uniform potential difference across a capacitor. Understanding the role of resistivity and conductivity can also enhance the comprehension of how materials within capacitors affect their overall performance and efficiency.

IB Physics Tutor Summary: In summary, a capacitor's charge and its voltage are directly linked - as one goes up, so does the other, described by the formula Q=CV. Capacitance measures how much charge a capacitor can hold for each volt applied. A higher voltage means more charge is stored. This relationship is straightforward and constant, making it easy to understand how capacitors store electrical energy.