Download Capacitance

Capacitance
• The potential of a conductor and the charge
on it are directly proportional to eachother
CAPACITANCE
• The Capacitance of a conductor is the ratio of
the charge on the conductor to its potential,
defined as: C = Q/V
• Where C is a constant
• The value of C depends on the size and shape
of the conductor.
• Symbol: C
• A capacitor is an electrical device used to store
charge (Q)
• Unit: Farad (F)
• Picture a water container.
• The amount of water the container can hold (its
capacity) will depend on – among other things –
how quickly the water level rises when water is
poured in; if the water level rises rapidly it
suggests the container must be quite narrow and
therefore may not hold much water.
• We would deduce that the container had a small
‘capacitance’.
Capacitors!
• A capacitor is similar to a battery but they
work in different ways.
• Inside the capacitor, the terminals connect to
two metal plates separated by a nonconducting substance, or dielectric.
• In theory, the dielectric can be any nonconductive substance. However, specific
materials are used that best suit the
capacitor's function. Mica, ceramic, cellulose,
porcelain.
What happens???
• The plate on the capacitor that attaches to the
negative terminal of the battery
accepts electrons that the battery is producing.
• The plate on the capacitor that attaches to the
positive terminal of the battery loses electrons to the
battery.
• Once it's charged, the capacitor has the
same voltage as the battery
• Here you have a battery, a light bulb and a
capacitor. If the capacitor is pretty big, what you
will notice is that, when you connect the battery,
the light bulb will light up as current flows from
the battery to the capacitor to charge it up. The
bulb will get progressively dimmer and finally go
out once the capacitor reaches its capacity. If you
then remove the battery and replace it with a
wire, current will flow from one plate of the
capacitor to the other. The bulb will light initially
and then dim as the capacitor discharges, until it
is completely out.
To show that a Charged Capacitor
stores Energy
1. Set up as shown.
2. Close the switch to charge the capacitor.
3. Remove the battery and connect the
terminals together to ‘short’ the circuit.
4. The bulb will flash as the capacitor
discharges, showing that it stores energy
Farads
• A 1-farad capacitor would typically be pretty
big. It might be as big as a can of tuna or a 1liter soda bottle, depending on the voltage it
can handle. For this reason, capacitors are
typically measured in microfarads
• An electrical capacitor can be compared to this
water container and the rate at which the potential
of the capacitor increases gives us an indication of
how much charge the capacitor can hold; if
putting a small charge on it raises its potential
considerably, then its capacitance must be small.
• Remember ‘raises its potential considerably’
means that a lot more work needs to be done to
bring further charge up to it.
• So for example if a capacitor has a capacitance
of 2 farads, then putting a charge of 6
coulombs on it will increase its potential by 3
volts (from C = Q/V, so V = Q/C).
• However if the capacitor had a capacitance of
200 farads, putting a charge of 6 coulombs on
it would only raise its potential by 0.03 volts.
Energy stored in a charged Capacitor
• The energy stored (W) in a charged
capacitor is given by:
• W = ½ CV2
Why should I care about Capacitors?
• Uses: Radio,
• Capacitive Touch Screens
• One of the more futuristic applications of capacitors is
the capacitive touch screen. These are glass screens
that have a very thin, transparent metallic coating. A
built-in electrode pattern charges the screen so when
touched, a current is drawn to the finger and creates a
voltage drop. This exact location of the voltage drop is
picked up by a controller and transmitted to
a computer. These touch screens are commonly found
in interactive building directories and more recently in
Apple's iPhone.
• The difference between a capacitor and a battery is
that a capacitor can dump its entire charge in a tiny
fraction of a second, where a battery would take
minutes to completely discharge. That's why the
electronic flash on a camerauses a capacitor -- the
battery charges up the flash's capacitor over several
seconds, and then the capacitor dumps the full charge
into the flash tube almost instantly. This can make a
large, charged capacitor extremely dangerous -- flash
units and TVs have warnings about opening them up
for this reason. They contain big capacitors that can,
potentially, kill you with the charge they contain
The value of Capacitance depends on
the shape and size of the plates
• This can be given by the formula:
• C=ƐA /d
• Ɛ= permitvity of the dielectric
• A= area of the plates
• D= distance of the
Example
• The area of overlap of the plates of an air
space capacitor is 20cm2. the distance
between the plates is 1mm.
• Given Ɛ = 8.9x10-12 Fm-1, find the
capacitance of the capacitor.
1.[2007]
• Calculate the energy stored in a 5 μF capacitor
when a potential difference of 20 V is applied
to it.
1.[2005]
• A capacitor of capacitance 100 μF is charged
to a potential difference of 20 V. What is the
energy stored in the capacitor?
1.[2002]
• How much energy is stored in a 100 μF
capacitor when it is charged to a potential
difference of 12 V?
A capacitor of capacitance 0.47uF
carries a charge of 2.0 uC. Calulate the
potential diff between the plates and
the energy stored
Formula Manipulation
• A capacitor has a capacitance of 6.3uF. What is
the charge on the plates when the energy
stored is 0.44 mJ?
To Demonstrate the Factors
affecting the Capacitance of a
Parallel Plate Capacitor
1. Connect the two parallel plates to a digital multi-meter
(DMM) set to read capacitance. Note the capacitance.
2. Increase the distance between them – note that the
capacitance decreases.
3. Move one plate slightly to the side (decreasing the overlap
area) – note that the capacitance decreases.
4. Place different slabs of insulating material between the
plates – note that the capacitance is lowest when nothing
(air) is between the plates
Ɛ= permittivity of the dielectric
• Ɛ= Ɛr x Ɛo
• Where Ɛr is relative permittivity
• And Ɛo is permittivity of free space