Capacitors - AP Physics C: Electricity and Magnetism

$C = \frac{\varepsilon A}{d}$. Capacitance depends on area $A$, distance $d$, and permittivity $\varepsilon$.

Time to reach $63%$ of final value. Characteristic time for exponential charging or discharging process.

Increases capacitance. Dielectric constant $k > 1$ multiplies the capacitance.

Farad (F). Named after Michael Faraday, represents charge per unit voltage.

$\tau = RC$. Product of resistance and capacitance determines charging rate.

$U = \frac{1}{2}CV^2$. Energy is proportional to capacitance and voltage squared.

Increases capacitance. Dielectric material increases capacitance by factor $k$.

$Q = CV$. Fundamental relationship between charge, capacitance, and voltage.

$V(t) = V_0 e^{-t/RC}$. Exponential decay from initial voltage with time constant $RC$.

$C_{\text{eq}} = C_1 + C_2 + \dots$. Parallel capacitors combine by direct addition of values.

$C_{\text{eq}} = C_1 + C_2 + \dots$. Parallel capacitors add directly like series resistors.

Capacitance increases. From $C = \frac{\varepsilon A}{d}$, capacitance is directly proportional to area.

Stored energy doubles. From $U = \frac{1}{2}CV^2$, energy is directly proportional to capacitance.

$Q = CV$. Fundamental relationship defining capacitance as charge per voltage.

Failure of dielectric under high voltage. Electric field exceeds dielectric strength, causing material failure.

$U = \frac{1}{2}CV^2$. Energy stored is half the product of capacitance and voltage squared.

$W = \frac{1}{2}CV^2$. Work equals energy stored in the electric field.

$u = \frac{1}{2}\varepsilon E^2$. Energy density depends on permittivity and electric field squared.

$U = \frac{1}{2} \frac{Q^2}{C}$. Alternative energy formula using charge instead of voltage.

Increases equivalent capacitance. Parallel connection sums individual capacitances.

$E = \frac{V}{d}$. Electric field equals voltage divided by plate separation.

Capacitance. Dielectric constant directly multiplies the capacitance value.

Decreases equivalent capacitance. Series connection reduces total capacitance below smallest value.

$V = \frac{Q}{C}$. Voltage equals charge divided by capacitance.

$Q = CV$. Charge is proportional to both capacitance and voltage.

Increases capacitance. From $C = \frac{\varepsilon A}{d}$, smaller $d$ increases capacitance.

Decreases the electric field. Dielectric reduces field by factor of dielectric constant $k$.

$D = \varepsilon E$. Displacement field relates permittivity to electric field strength.

Permittivity of free space. Fundamental constant relating electric field to electric displacement.