C = q/v

Definition

The equation $$c = \frac{q}{v}$$ defines capacitance, where 'c' is the capacitance measured in farads (F), 'q' is the electric charge stored in the capacitor, and 'v' is the voltage across the capacitor. This relationship highlights how a capacitor's ability to store charge is directly proportional to the charge itself and inversely proportional to the voltage applied. Understanding this equation helps clarify how capacitors function in electrical circuits, especially when analyzing energy storage and behavior under different configurations.

5 Must Know Facts For Your Next Test

1. Capacitance is dependent on both the physical characteristics of the capacitor, such as plate area and separation distance, and the type of dielectric material used.
2. In practical terms, a higher capacitance means a capacitor can store more charge at a given voltage, making it essential for applications like smoothing out voltage fluctuations.
3. Capacitors can be connected in series or parallel; their overall capacitance behaves differently depending on the configuration, affecting how charge and voltage distribute across them.
4. Energy stored in a capacitor can be calculated using the formula $$E = \frac{1}{2}cv^2$$, showing the relationship between energy, capacitance, and voltage.
5. Capacitance is a fundamental concept in many electronic devices, playing a crucial role in timing circuits, filters, and energy storage systems.

Review Questions

• How does changing the voltage affect the charge stored in a capacitor as described by the equation c = q/v?
  • According to the equation $$c = \frac{q}{v}$$, if you increase the voltage 'v' across a capacitor while keeping capacitance 'c' constant, the charge 'q' stored must also increase proportionally. This means that for a given capacitor, higher voltages allow for greater amounts of charge to be stored. Conversely, if the voltage decreases, so does the amount of charge that can be stored.
• In what ways do series and parallel configurations of capacitors influence total capacitance compared to individual capacitances?
  • When capacitors are connected in series, their total capacitance decreases according to the formula $$\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + ...$$ This happens because each capacitor shares the same charge but has different voltage drops across them. In contrast, connecting capacitors in parallel results in an additive effect on capacitance: $$C_{total} = C_1 + C_2 + ...$$ This configuration allows for greater total charge storage at a given voltage because each capacitor adds its ability to hold charge.
• Evaluate how varying dielectric materials between capacitor plates affects both capacitance and energy storage potential.
  • Different dielectric materials have varying properties that influence how much electric field strength is reduced between capacitor plates. A material with a higher dielectric constant increases capacitance according to $$c = \frac{\epsilon A}{d}$$ where 'A' is plate area and 'd' is separation distance. Consequently, higher capacitance means more charge can be stored at a given voltage. This directly impacts energy storage potential since more stored charge translates to increased energy stored based on the formula $$E = \frac{1}{2}cv^2$$. Thus, selecting an appropriate dielectric material can enhance both performance and efficiency in electronic applications.

Related terms

Capacitor: A component that stores electrical energy in an electric field, characterized by its capacitance value.

Voltage: The electric potential difference between two points, which drives the flow of electric current.

Dielectric: An insulating material placed between the plates of a capacitor that increases its capacitance by reducing the electric field strength.