21 - Capacitance

what is a capacitor

explain the structure of a capacitor

- an electrical component in which charge is separated and stored on two metallic plates

- metallic plates are separated with an insulator called a dielectric

What is a dielectric?

what are some examples of dielectrics?

-a non-conducting material that is placed between the conducting plates of a capacitor

- air, paper, ceramic or mica

how does a capacitor gain and store its charge?

how does the dielectric affect the current of the circuit and the maximum charge stored by the capacitor?

what is the net charge across the whole capacitor?

- capacitor connected to power supply

- brief current flows which remove electrons off of one plate and deposit on the other but cannot travel between the plates

- first plate acquires positive charge, second plate aqcuires negative charge

- due to the conservation of charge, the charges will be equal and opposite

- current will flow until the P.D. across the capacitor is equal to the e.m.f.

- net charge on the capacitor is zero.

define capacitance

what is the equation?

capacitance is defined as the amount of charge stored per unit potential difference

- C = Q/V

capacitance - farads

charge - coulombs

potential difference - volts

do capacitors in parallel store more or less charge than capacitors in series?

- for two capacitors in parallel, their capacitance is greater than their individual capacitance so the combination will store more charge for a given p.d.

- when connected in series, the combines capacitance is less than their individual capacitances

derive capacitors in parallel

what value is constant in C=Q/V

in parallel, potential difference is constant

Q = Q1 + Q2...

derive capacitors in series

what value is constant in C=Q/V

in series, charge is constant

V = V1 + V2...

what does the energy stored in a capacitor depend on

- initial P.D. across it

- the value of the capacitance

how is the energy transferred from the power supply to the capacitor

- each electron moving toward the negative place experiences a repulsive electrostatic force from the electrons already on it

- similarly, each electron leaving the positive plate will experience an attractive electrostatic force towards the plate

- external work has to be done to push the electrons to the negative plate and pull them from the positive plate

- this work (energy) comes from the power supply and is therefore stored in the capacitor

what is the work done to increase the charge of a capacitor by a small amount?

how is this represented on a graph?

- the small amount of work done to increase the charge stored in the capacitor by a small amount where the p.d. does not vary significantly

- △W = V x △Q

what is the total energy stored in a capacitor formula?

how is it shown on a graph?

the total energy stored in the capacitor is the total area under the P.D. - Charge graph

= W = ½QV

what other equations can be derived from the work done equation for a capacitor

W = ½QV

W = ½(Q²/C)

W = ½V²C

explain the process of discharging a capacitor through a resistor in terms of current, p.d., charge and charge difference and electric field

- initially capacitor has a large charge difference between the plates creating a strong electron field

- the strong electric field repels electrons from negative plate to positive plate forcing them through the circuit (∴ through the resistor)

- as current flows, the negative plate loses electrons, and the positive gains electrons

- reducing charge difference means weaker electric field meaning weaker force on electrons meaning decreasing current

- this means p.d. across the plate is also decreasing

- when both plate has equal charge, electric field is no more and current stops flowing

∴ charge decreases, P.D. decreases, I decreases

graphs for exponential decay in capacitor discharge

what are the formulas for the discharging of capacitors for current, p.d., and q

What is the time constant?

what is the formula?

The time taken for a capacitor to discharge to 37% its peak voltage/charge to 63% its peak voltage

τ=CR

do capacitors release energy quickly or slowly?

what is an example?

capacitors release stored energy very quickly & thus generate high-output power

- camera flash

- certain particle accelerator

is domestic electricity AC or DC

how can a rectifier circuit give this the smooth DC?

what two components are necessary?

what can reduce the ripple effect?

domestic electricity is supplied as AC

rectifier circuits used to convert this alternating input into a smooth direct current

- add a diode to ensure the current is unidirectional (one direction)

- add a capacitor to smooth out the voltage to almost a constant value (rippler effect)

- the ripple effect can be reduces with a large time constant

explain how to charge up a capacitor; explain the change in values of p.d., charge and current

- maximum current flows

- capacitor begins to charge

- p.d. across the capacitor increases from zero

- The capacitor will be fully charged with the same p.d. across power supply

- current will be zero when capacitor is charged

- current decreases exponentially

charging capacitors graphs

equations for charging capacitors