# CAPACITORS

```CAPACITOR BASICS
OBJECTIVE
๏ฑUnderstand that capacitance is defined as C =Q/V and be
able to use this equation.
๏ฑBe able to use the equation W = 1/2 QV for the energy
stored by a capacitor, be able to derive the equation from
the area under a graph of potential difference against
charge stored and be able to derive and use the equations
W = 1/2
๐ช๐ฝ๐
and W=
๐
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๐ธ๐ /๐ช
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๏ฑ A Capacitor is a two-terminal,
electrical component used to store
store electrical energy .
.
๏ฑ Along with resistors and inductors,
they are one of the most fundamental components we use
in a circuit.
Capacitance
The ability of any object to โstoreโ electric charge is
described as capacitance.
An electrical component designed to have significant
capacitance is called a capacitor.
Capacitors are useful components of circuits because of
their ability to store small amounts of energy.
Parallel plate capacitors
Parallel metallic plates separated by an insulator are the
most common kind of capacitor. When a p.d. is connected
across the plates they will gain equal and opposite charge.
Qw
CHARGING OF CAPACITOR
When the power supply is
connected, electrons flow from
negative terminal to positive
terminal.
Electrons cannot cross the gap
between the plates so they build up
in plate B connected to negative
terminal.
A
B
Qw
CHARGING OF CAPACITOR
Electrons in plate B repel the
electrons in the plates A connected
to the positive terminal and makes
the electrons flow towards the
positive of the battery.
Now plate A become positively
charged and plate B is negatively
charged.
A
B
Qw
CHARGING OF CAPACITOR
๏ถ Electrons in plate B repel the
electrons in the plates A connected
to the positive terminal and makes
the electrons flow towards the
positive of the battery.
๏ถ Now plate A become positively
charged and plate B is negatively
charged.
A
B
Qw
CHARGING OF CAPACITOR
๏ถ The attraction between the
opposite charges across the gap
creates an electric field between
the plates.
๏ถ This process of this charging
stops when p.d. across the plates
has risen to become equal to the
p.d. across the battery.
A
B
Qw
CHARGING OF CAPACITOR
๏ถ At this stage the capacitor is
acting like a store of charge.
A
B
Only charge a capacitor to or
below its specified voltage
rating. Charging a capacitor to a
voltage beyond its voltage rating
can destroy the capacitor.
Discharging of capacitor occurs when charged
capacitor is connected to a load in a circuit.
Calculating capacitance
๏ถ The amount of charge a capacitor can store, per
๐ธ
volt across it is called as its capacitance. C =
๐ฝ
๏ถ 1F = 1J / 1V
๏ถ Capacitance is measured in farads(F)
๏ถ This is a large unit, so that ฮผF and pF are in common
use in practical lab works.
๏ถ The capacitance of parallel plates increases if the plates
have larger area and are closer together. Adding a
suitable insulator, with high permittivity, between the
plates also increases capacitance.
Effect of insulators in a capacitor
A capacitor with a an insulators stores the same charge as
one without an insulators, but at a lower voltage. Therefore
a capacitor with a insulators in it is more effective.
Charging a capacitor
In this case, the capacitor charges up to 9
volts, since it's connected to a 9-volt
battery. Many of the times while charging a
capacitor, a resistor is used in series with
the capacitor and voltage source to decrease
the amount of current that flows through
the capacitor, so that the capacitor isn't
damaged. This is usually recommended.
๏ฑ 3× ๐๐๐ F
๏ฑ 3.6× ๐๐๐ ๐ช
Coulomb meter
A Coulomb meter is a tool for measuring the
electrostatic charge of a material.
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There are other versions of
this formula. Since Q = CV,
we
get Ue = (1/2)CV2. Also,
Ue = (1/2)QV.
1.7× 10โ5 F
1.0× 10โ3 ๐น
1.1× 10โ3 ๐
Capacitor discharge curves
๏ฑ Unless it is required to discharge a
capacitor very quickly, a resistor will
be included in any capacitor circuit in
order to control the rate of
discharging (or charging).
๏ฑ The charging or discharging of a
capacitor can be observed and recorded
by measuring either the changing p.d.
across it, or the changing current
through the resistor.
When a capacitor discharges, the rate of discharge will be highest
at the beginning because the amount of charge on the plates is
greatest, so that the free electrons experience the greatest
forces.
Figure shows a typical discharge graph. Note
that it may represent the variation with time
of the discharge current, or the voltage acros
the capacitor, or the charge remaining on the
capacitor plates
During a capacitor discharge, the charge, voltage and current
decrease exponentially. That is, their values fall by the same
fraction in equal time intervals.
The rate of discharge at any time (which
could be determined from the gradient of
the graph at that moment) is proportional
to the value of the quantity at that
moment. For example, - ฮQ/โ๐ โ Q.
Current: Initially, the electric field from the
supply sends a large surge of electrons onto
the capacitor, so the current starts at its
maximum. After a little time, the electrons
already stored on the capacitor reduce the
effective push (or electric field) from the
supply, so the charge movement is reduced โ
a smaller current. Eventually, the capacitor
has as much charge as the 6 V supply can
push onto it, and the mutual repulsion
of electrons already stored stops any further
charge moving onto the capacitor; the
current falls to zero.
Potential difference(p.d):
Initially, the capacitor has no charge on
it, so its p.d. is zero. After a little time,
the charge stored across the capacitor
creates some p.d., which could be
measured using a voltmeter. Eventually,
the capacitor has as much charge as the
6 V supply can push onto it, which will be
when it has also reached a voltage of 6 V,
and it will remain at this value.
Charge: Initially, the capacitor has no
charge on it. The current starts at its
maximum so, after a little time,
some charge is stored on the capacitor.
The reduced current continues to add
charge to the capacitor but at a
slower rate. Eventually, when the current
reaches zero, no more charge is added to
the capacitor, and the amount on it
remains constant at its maximum, CV
Basic exponential decay curve as per fig B(a): initial current is 0.6 mA.
This should fall to 0.22 mA in 0.5 s. At 1 s, the current has dropped to
0.08 mA, then at 1.5 s it is 0.03 mA, finishing at 0.01 mA by 2 s.
Depending on scale, it is likely that the final half second should look
horizontal along zero mA.
How could we make light lamp for longer , for
longer given the same power supply?
๏ฑ Store more charge on the capacitor
๏ฑ Decrease the rate at which the
capacitor discharge.
๏ฑ Increase the capacitance C, will increase the charge
stored . Q=CV
๏ฑ The charge will flow more slowly if the bulb resistance
R is greater.
Time constant
Rate of change of a capacitor can be gained by working out
time constant (๐)
๐ = ๐น๐ช
Time constant in C-R circuit tells us how many seconds it
takes for the current to fall to 37% of its starting
value.
Time constant determines how long it takes for a
capacitor to change or discharge over one time constant.
A 15ฮผF-capacitor is connected to a 9.6-V battery. Calculate (a) the
charge accumulation and (b) the energy stored in it
(a) Q = CV ; Q = (15ฮผF)(9.6 V) = 144ฮผC
(b) Ue = (1/2)QV ; Ue = (1/2)(144ฮผC )(9.6V) = 690 ฮผJ
Capacitor Discharge Equation
Derivation
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