AP Physics 2 capacitors and dielectrics

What is a capacitor?

A capacitor is a two-terminal electrical component that stores electrical energy in an electric field, typically consisting of two conductive plates separated by an insulator.

Capacitance formula

Capacitance ($\displaystyle C$) is defined as $\displaystyle C = \\frac{Q}{V}$, where $\displaystyle Q$ is the charge stored and $\displaystyle V$ is the voltage across the capacitor.

Unit of capacitance

The unit of capacitance is the farad (F), which is defined as one coulomb per volt ($\displaystyle 1 ext{ F} = 1 ext{ C/V}$).

True or False: Capacitors can only store AC.

False. Capacitors can store both AC and DC energy, but they charge and discharge differently depending on the type of circuit.

Fill in the blank: The energy stored in a capacitor is given by ______.

The energy stored in a capacitor is given by $\displaystyle U = \\frac{1}{2}CV^2$, where $\displaystyle U$ is energy, $\displaystyle C$ is capacitance, and $\displaystyle V$ is voltage.

Parallel vs Series: Capacitance

In parallel: $\displaystyle C_{total} = C_1 + C_2 + ...$ In series: $\displaystyle \\frac{1}{C_{total}} = \\frac{1}{C_1} + \\frac{1}{C_2} + ...$

What happens when a dielectric is inserted?

Inserting a dielectric increases the capacitance by a factor equal to the dielectric constant ($\displaystyle K$): $\displaystyle C' = KC$, where $\displaystyle C'$ is capacitance with the dielectric.

Capacitor charging graph shape

The voltage across a charging capacitor rises exponentially, approaching the supply voltage asymptotically.

Energy density in a capacitor

The energy density ($\displaystyle u$) in a capacitor is given by $\displaystyle u = \\frac{1}{2} \\frac{E^2}{\epsilon_0}$, where $\displaystyle E$ is the electric field and $\displaystyle \epsilon_0$ is the permittivity of free space.

What is equivalent capacitance?

Equivalent capacitance is the total capacitance of a combination of capacitors, determined by how they are connected (series or parallel).

True or False: Capacitors block DC current.

True. Capacitors block DC current once fully charged, allowing AC to pass through.

Charging time constant

The time constant ($\displaystyle \tau$) for a capacitor is $\displaystyle \tau = RC$, where $\displaystyle R$ is the resistance and $\displaystyle C$ is the capacitance.

Dielectric constant symbol

The dielectric constant is represented by the symbol $\displaystyle K$, which varies for different materials.

Capacitance of a parallel plate capacitor

The capacitance of a parallel plate capacitor is given by $\displaystyle C = \\frac{\epsilon_0 A}{d}$, where $\displaystyle A$ is plate area and $\displaystyle d$ is the separation distance.

Energy stored in a capacitor example

For a capacitor with $\displaystyle C = 2 ext{ F}$ and $\displaystyle V = 10 ext{ V}$, energy $\displaystyle U = \\frac{1}{2} C V^2 = 100 ext{ J}$.

True or False: Capacitors can store electric charge indefinitely.

False: Capacitors can only store charge temporarily. They discharge over time due to leakage currents and circuit connections.

What is a dielectric?

A dielectric is an insulating material placed between the plates of a capacitor, which increases its capacitance by reducing the electric field.

True or False: Dielectrics always increase capacitance.

True. Dielectrics increase capacitance by reducing the effective electric field between the plates.

Formula for capacitance with a dielectric?

The capacitance with a dielectric is given by: $\displaystyle C = \frac{K imes ext{A}}{d}$, where K is the dielectric constant.

Effect of dielectric on electric field?

Dielectrics reduce the electric field $\displaystyle E$ in a capacitor by a factor of the dielectric constant $\displaystyle K$: $\displaystyle E_{new} = \frac{E_{0}}{K}$.

What is dielectric constant (K)?

The dielectric constant (K) is a measure of a material's ability to store electrical energy in an electric field.

Fill in the blank: K for air is approximately ____.

K for air is approximately 1.

Comparison: Vacuum vs. dielectric material.

Vacuum has a dielectric constant of 1, while dielectric materials have K > 1, increasing capacitance.

Cause → Effect: Inserting a dielectric increases capacitance.

Cause: Inserting a dielectric. Effect: Increases capacitance and reduces electric field strength.

What happens to stored energy with a dielectric?

Stored energy increases because energy $\displaystyle U = \frac{1}{2}CV^2$ and $\displaystyle C$ increases with dielectric.

True or False: Dielectrics can be polarized.

True. Dielectrics can become polarized, aligning their dipoles with the electric field.

Formula for energy stored in dielectric capacitor?

Energy stored is: $\displaystyle U = \frac{1}{2} C V^2$, with $\displaystyle C$ modified by dielectric constant.

What is breakdown voltage?

Breakdown voltage is the maximum voltage that can be applied across a dielectric before it becomes conductive.

Effect of temperature on dielectrics?

Increasing temperature generally decreases the dielectric constant, affecting capacitance.

Fill in the blank: Teflon has a dielectric constant of approximately ____.

Teflon has a dielectric constant of approximately 2.1.

How does dielectric strength relate to safety?

Higher dielectric strength indicates a material can withstand higher voltages, ensuring safety in capacitors.

Dielectric loss tangent definition?

The dielectric loss tangent is a measure of energy loss in the dielectric material, represented as $\displaystyle an( heta)$.