Module 5 Paper 2 Flashcards
Definition of a Capacitor
capacitor is an electrical component that stores charge on two separated metallic
plates.
dielectric
An insulator, sometimes called a dielectric, is placed between the plates to
prevent the charge from travelling across the gap.
capacitance,
The capacitance, πΆ, is defined as the charge stored, π, per unit potential difference, π,
across the two plates. Therefore we can write
C = Q/V
measured in Farads, F (CV-1)
capacitor is connected to a DC power supply, e.g. a cell or battery, there is a brief
current
power supply draws electrons from one plate and deposits them on the
other plate. This leaves the first plate with charge +ππ and the second with charge β ππ.
These charges will be equal and opposite due to the conservation of charge. Current will
flow in the circuit until the potential difference between the plates is equal to that of the
electromotive force or e.m.f. of the power supply.
dielectric has another purpose:
to increase the capacitance of the device by
polarizing in the electric field and effectively increasing the charge stored on the plates.
electrical permittivity
which
describes its ability to polarize and strengthen the charge storage capability of the
device.
Capacitors in Series
Capacitors in Parallel
Energy Stored in a Capacitor
Work must be done by the power supply to deposit negatively charged electrons onto
the negative plate as like charges repel according to Coulombβs law Equally, work is done to remove electrons from the positive plate as negative
charges are attracted to positive regions
Energy Stored in a Capacitor GRAPH
Energy Stored in a Capacitor GRAPH
electric field
region of space in which charged particles are subject to an electrostatic
force
Applications of Capacitors
store and discharge large quantities of energy in a short time
period. This makes them useful for short pulses of energy such as camera flashes and
touch screens where a short finger press leads to a large buildup of energy in a
capacitor
capacitors are used in the process of converting alternating current (AC) into
direct current (DC)
Once a sinusoidal AC signal has passed through a full wave rectifier,
the current flows in one direction but varies as shown. The current can then be passed
through a smoothing circuit in which a capacitor stores energy as the p.d. rises and
discharges as it falls.
This can be used maintain a more constant current. The signal can then be passed
through another smoothing circuit and another until the voltage is effectively constant.
Discharging Capacitors
electrons packed onto the negative plate are
no longer subject to the e.m.f. which held them in such close proximity. They repel one
another and so flow round circuit dissipating electric energy as heat in the resistor. Once,
the charges on the negative and positive plates have equilibrated, there is no longer any
potential difference across the capacitor (ππ = 0) and the electrons cease to flow
resulting in the current dropping to zero.
time constant
The time constant over which this
discharging process occurs depends firstly on the capacitance and also on the
magnitude of the resistance in the discharging circuit.charge on the capacitor will have decreased to approximately 37% of its original value
lower resistance in dischgarging unit effect on circuit with a capacitance
The lower the resistance in the
discharging circuit, the higher the current can be as current is indirectly proportional tothe resistance from Ohmβs law (πΌ β 1/r). If the current is higher, then the charge on the
plates will fall to zero in a faster time as βπ = πΌt. Equally, the larger the capacitance the
larger the charge stored per unit potential difference.
Experimental Techniques to investigate Capacitor-Resistor Circuits
To investigate the charge or discharge of a capacitor a circuit with a DC power supply, a
capacitor, a resistor in series, an ammeter in series and a voltmeter in parallel are
needed. Data loggers can be used to collect the data in time as capacitors often discharge
very quickly. Plotting current and voltage with time in charging and discharging circuits
can be used to investigate of the exponential relationships between the variables
current and p.d. with time. The readings for the voltage and current should be taken at
set intervals which should be small compared to the time constant. This can then allow
for an experimental determination of the time constant. The experimental value could
then be compared to the theoretical value based on the values of the resistance and
capacitance
Dependence of Capacitance on Dimensions of the Capacitor
The capacitance of a parallel plate capacitor depends on the number of electrons that
can be stored on the negative plate and so is directly proportional to the area of the
plates, π¨π¨.
The attraction between charges on the negative plate and the positive plate
depends on the separation of the plates, ππ
. Therefore the capacitance is indirectly
proportional to π
π
so C = epsilon A/d
Electric field lines
point outwards from a positive charge or inwards
towards a negative charge as the direction of the field represents the direction of the
electrostatic force on a positive charge at that point.
strength of the field decreases
he radial distance or the distance away from the charge. This is shown by the decreasing
density of the field lines, the less tightly packed the field lines are the weaker the electric
field is at that point and the weaker the electrostatic force will be on a given charge
Electric Field Strength
The strength of an electric field, πΈ is defined as the force, πΉ applied per unit charge π on an
object and is expressed as: E = F/Q
Coulombβs law
states that any two point charges exert an electrostatic force between them
that is proportional to the product of their charges and inversely proportional to the square
of the distance between them.
permittivity of free space
Permittivity is a constant that
defines the ability of a material to become polarized and store charge. The permittivity of
free space is the permittivity of a vacuum and as there is no matter in a vacuum to become
polarized this is the lowest value possible.
Electric Field of a Point Charge
Using Coulombβs law and the formula for electric field strength, it is possible to form an
expression for the electric field of a point charge. To do this we must imagine bringing a
small test charge of charge, π, towards a large point charge of charge, π, such that the effect
of the test charge on the point charge is negligible i.e. the test charge does not cause the
point charge to move.
Uniform electric field
A uniform field is a field which has no dependence upon position i.e. the field is constant in
space. A uniform electric field is produced between two parallel oppositely charged plates. A
particle between such plates is subject to a constant force no matter where it resides
between the plates.
Work Done
Work done is a measure of the energy transferred to an object by a force. It is the product of
the force and the distance over which the force acts in the direction of the force. Therefore, work is done when moving a charge in an electric field. The work done per unit
charge in moving a charge from one point to another in the field defines the potential
difference between those two points
w = VQ = Fd = EQd
Millikanβs oil drop experiment
oil droplets are charged with a small electric charge and
allowed to fall under gravity in a vertical uniform electric field. The electric field is
generated by two oppositely charged parallel plates to ensure that it is uniform. As these
drops fall, the voltage between the plates can be increased and to produce a larger electric
field in the gap. This produces an upward acting force which can be increased to balance
with the force of gravity. When the oil drops hover in midair, we can deduce that the weight
force downwards must be equal to the force of the electric field upwards as there is no
acceleration. accurate determination of the
elementary charge.
mg = eq
V = mgd/ne
Work done on Point Charges
work is done when a charge, π, is brought in from infinity to a distance π from a point
charge, π
Definition of the Magnetic Field
A magnetic field is a region of space in which moving charged particles are subject to a
magnetic force. Magnetic fields are also created by moving charges and it is the interaction
of two magnetic fields that results in a magnetic force.
permanent magnet
object made from a magnetized material that creates its own
persistent magnetic field the
electrons in the material move in an ordered way to produce an overall magnetic field
around the material
The magnetic field of bar magnets is often demonstrated using iron filings (iron cut into
small pieces about the size of grains of sand). Iron, as a ferromagnetic material, has the
property that in a magnetic field its atoms tend to align with the field such that its electrons
move in an ordered way. This then creates an induced magnetic field in the iron so that the
induced north pole points in the direction of the magnetic field at that point in space
electromagnet
uses the field generated by a current carrying wire to create a large
magnetic field that can be magnified or reduced by raising or lowering the current.
Electromagnets, made fromβ¦.
coils of wire (often called solenoinds), act as bar magnets when
an electric current passes through them. Often, the coil is wrapped around a soft core such
as mild steel, which causes an induced field in the core and greatly enhances the magnetic
field produced by the coil. Additionally, a coil with more turns causes a greater magnetic
field.
magnetically soft and hard metarial
magnetically soft materials like iron an be magnetized but do not stay magnetised away from the external field and magnetically hard do
magnetic flux density of a current carrying wire
each circular line of flux around the wire has a much larger radius than the previous line so the magnetic flux density decreases drastically
magnetic flux density of a current carrying wire
each circular line of flux around the wire has a much larger radius than the previous line so the magnetic flux density decreases drastically
right hand rule
point thumb in direction of current and fingers wrap in the direction of the magnetic field
right hand rule
point thumb in direction of current and fingers wrap in the direction of the magnetic field
current coming into the page
current going downward is notated with an x,
current coming up is noted with a dot
left hand rule
when a current carrying wire is placed into a magnetic field it experiences a force due to the interaction of its magnetic field and external field.
(index) = magnetic field
(middle) = current
thumb = resultant motion
force on current carrying wire
interaction is greatest when current points perpindicular to the magnetic field.
F = BILsinx
Velocity selectors
Velocity selectors use a combination of magnetic and electric fields to isolate particles with a specific velocity. This is possible due to the fact both the magnetic and electric forces are charge dependent.
magnetic flux density
magnetic flux per unit area
magnetic flux linkage
for a uniform magnetic field magnetic flux = BA cosx
electromagnetic induction
when a current is induced due to a change in the magnetic flux linkage current is produced by moving the wire or varying field strength
faradays law
induced emf is proportional to the rate of change of magnetic flux linkage
Lenz law
induced emf is generated in a direction that so it opposes the change that produced it
AC generator how it function
utilises a coil of wire placed in a constant uniform magnetic field. The coil is then rotated and so the area perpendicular to the magnetic field is constantly changing as the sine of the angle between the field and the plane of the coil. This changing magnetic flux linkage causes an alternating current to be induced in the wire.
magnetic flux linkage and induced emf vary in time as the coil is rotated at a constant angular velocity.
step up and step down transformers
either raise or lower the voltage of the alternating current by using electromagnetic induction. the alternating current in the primary coil induces varying magnetic flux in the iron core. induces current in the secondary coil .
(vp)(t)/(ns) = magnetic flux
