Capacitance

Series Resistors

Formulas

Factors affecting capacitance

Plate Area

Larger area --> more field flux for a given force

Plate Spacing

With power supply
Closer spacing --> greater field force --> greater field flux

Permittivity of Dielectric

Dielectric is an electrical insulator that can be polarised when in an electric field

positive end of the molecule moves in the direction of the field

Dielectric

Prevent plates from touching

Reduce possibility of shorting out

One more

Types of Capacitors

$C= \varepsilon_0\frac{A}{d}$
$\varepsilon_0$ is permittivity of free space $8.85\times10^{-12}$
$A$ is surface area of plates
$d$ is separation of plates

$E=\frac{1}{2}CV^2$

Electrolytic Capacitor

Capacitor layer is rolled up

Sum of Capacitance

Parallel
$C_T=C_1+C_2+C_3…$

Series
$C_T=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}…$

Series Resistors

Parallel Resistors

$Q=CV$

Capacitor

Polarity follows direction of conventional current

Capacitor discharges if connected in parallel and retains energy if connected in series

Without power supply
larger plate separation --> same charge, lower capacitance, higher voltage

Charging

Charging rate

Resistance of circuit

Capacitance of capacitor

Process

Small resistance --> Fast charging rate

Electrons flow from ⛔ terminal of ⚡ to one plate of capacitor and from other plate to ➕
Potential difference across capacitor and charge increases at a decreasing rate

Current and rate of rise of potential difference both fall exponentially as electrons on ⛔ plate repels new electrons and stops current

Current stops flowing when potential difference across capacitor equals potential difference across supply voltage

Capacitor fully charged

Current-time graph

Area under graph is charge

Discharging Process

$q=q_0e^{-\frac{t}{\tau}}$

Time constant:
Time taken for discharging capacitor to fall to 36.8% (e^-1
Time taken for charging capacitor to rise to 63.2%)
$\tau=RC$

Half-Life
Time taken for charge to decrease to half its initial value
$\tau=\frac{T_{1/2}}{\ln 2}$

can be used to estimate time constant of graph

$I_0=\frac{q_0}{\tau}$

$v=v_0e^\frac{t}{\tau}$

charge per unit voltage that can be stored on capacitor