Download PHYSICS SAE 7

Physics Subject Area
Test
ELECTRICITY & MAGNETISM
Electric Charge and Electrical Forces:
*Electrons have a negative electrical charge.
*Protons have a positive electrical charge.
*These charges interact to create an electrical force.
*Like charges produce repulsive forces
–they repel each other
*Unlike charges produce attractive forces
–they attract each other
*
A very highly simplified model of an atom has most of the mass in a small,
dense center called the nucleus.
The nucleus has positively charged protons and neutral neutrons.
Negatively charged electrons move around the nucleus at much greater
distance.
Ordinary atoms are neutral because there is a balance between the
number of positively charged protons and negatively charged electrons.
Electrostatic Charge:
*Electrons move from atom to atom to
create ions.
*positively charge ions result from the loss
of electrons and are called cations.
*Negatively charge ions result from the
gain of electrons and are called anions.
(A)A neutral atom has
no net charge
because the numbers
of electrons and
protons are balanced.
(B) Removing an
electron produces a net
positive charge; the
charged atom is called a
positive ion (cation).
(C) The addition of an
electron produces a net
negative charge and a
negative ion (anion).
The charge on an ion is called an
electrostatic charge.
*An object becomes electrostatically charged
by
*Friction, which transfers electrons between
two objects in contact,
*Contact with a charged body which results in
the transfer of electrons,
*Induction which produces a charge
redistribution of electrons in a material.
Electrical Conductors and Insulators
Electrical conductors are materials that can move electrons
easily.
* Good conductors include metals. Copper is the best
electrical conductor.
Electrical nonconductors (insulators) are
materials that do not move electrons easily.
Examples are wood, rubber etc.
Semiconductors are materials that sometimes
behave as conductors and sometimes behave as
insulators.
Examples are silicon, arsenic, germanium.
fundamental charge - the electrical charge on an electron
-has a magnitude of 1.6021892 X 10-19 C
(measured in coulombs).
coulomb - the charge resulting from the transfer of
6.24 x 1018 of the charge carried by an electron.
magnitude of an electrical charge (Q) is dependent upon
how many electrons (n) have been moved to it or away
from it.
Mathematically,
Q = n ewhere e- is the fundamental charge.
Coulomb’s law:
Electrical force is proportional to the product of the
electrical charge and inversely proportional to the
square of the distance.
This is known as Coulomb’s law.
F k
q1 q 2
d
2
where,
*F is the force,
*k is a constant and has the value of 9.00 x 109
Newtonmeters2/coulomb2 (9.00 x 10
9
Nm2/C2),
*q1 represents the electrical charge of object 1 and q2
represents the electrical charge of object 2, and
*d is the distance between the two objects.
Force Fields:
The electrical charge produces a force field, that is
called an electrical field since it is produced by
electrical charge.
Voltage is a measure of the potential difference
between two places in a circuit.
*Voltage is measured in joules/coloumb.
*The rate at which an electrical current (I) flows
is the charge (Q) that moves through a cross
section of a conductor in a give unit of time (t),
I = Q/t.
*the units of current are coulombs/second.
*A coulomb/second is an ampere (amp).
ELECTRICAL CIRCUITS
The CELL
The cell stores chemical energy and transfers it to
electrical energy when a circuit is connected.
When two or more cells are
connected together we call this
a Battery.
The cells chemical energy is
used up pushing a current round
a circuit.
What is an electric current?
An electric current is a flow of microscopic particles called
electrons flowing through wires and components.
+
-
In which direction does the current flow?
from the Negative terminal to the Positive terminal of a
cell.
*
* A simple circuit is a connection of batteries and resistors
that meets 2 criteria
1.
2.
All batteries are in series
The equivalent resistance of the entire circuit can be
obtained by repeated use of just the series and parallel
equivalent resistance formulas
simple circuits
Here is a simple electric circuit. It has a cell, a
lamp and a switch.
cell
wires
switch
lamp
To make the circuit, these components are connected
together with metal connecting wires.
simple circuits
When the switch is closed, the lamp lights up. This is
because there is a continuous path of metal for the
electric current to flow around.
If there were any breaks in the circuit, the current
could not flow.
circuit diagram
Scientists usually draw electric circuits using symbols;
cell
lamp
switch
wires
circuit diagrams
In circuit diagrams components are represented by
the following symbols;
cell
ammeter
battery
voltmeter
switch
motor
lamp
buzzer
resistor
variable
resistor
types of circuit
There are two types of electrical circuits;
SERIES CIRCUITS
PARALLEL CIRCUITS
SERIES CIRCUITS
The components are connected end-to-end, one
after the other.
They make a simple loop for the current to flow round.
If one bulb ‘blows’ it breaks the whole circuit and all the bulbs go
out.
PARALLEL CIRCUITS
The components are connected side by side.
The current has a choice of routes.
If one bulb ‘blows’ there is still be a complete circuit to
the other bulb so it stays alight.
measuring current
Electric current is measured in amps (A) using
an ammeter connected in series in the circuit.
A
measuring current
This is how we draw an ammeter in a circuit.
A
A
SERIES CIRCUIT
PARALLEL CIRCUIT
measuring current
SERIES CIRCUIT
• current is the same
at all points in the
circuit.
2A
2A
2A
PARALLEL CIRCUIT
• current is shared
between the
components
2A
2A
1A
1A
copy the following circuits and fill in the
missing ammeter readings.
3A
?
4A
?
3A
1A
?
4A
?
4A
1A
1A
?
measuring voltage
The ‘electrical push’ which the cell gives to the current
is called the voltage. It is measured in volts (V) on a
voltmeter
V
measuring voltage
Different cells produce different voltages. The
bigger the voltage supplied by the cell, the bigger the
current.
Unlike an ammeter a voltmeter is connected across
the components
Scientist usually use the term Potential Difference
(pd) when they talk about voltage.
measuring voltage
This is how we draw a voltmeter in a circuit.
V
SERIES CIRCUIT
V
PARALLEL CIRCUIT
measuring voltage
V
V
V
V
series circuit
• voltage is shared between the components
3V
1.5V
1.5V
parallel circuit
• voltage is the same in all parts of the circuit.
3V
3V
3V
measuring current & voltage
copy the following circuits on the next two
slides.
complete the missing current and voltage
readings.
remember the rules for current and voltage
in series and parallel circuits.
measuring current & voltage
a)
6V
4A
A
V
V
A
measuring current & voltage
b)
4A
6V
A
V
A
V
A
answers
a)
b)
4A
6V
6V
4A
6V
4A
4A
3V
2A
3V
4A
6V
2A
*
In electricity, the concept of voltage will be like pressure.
Water flows from high pressure to low pressure (this is
consistent with our previous analogy that
Voltage is like height since DP = rgh for
fluids) ; electricity flows from high voltage to low
voltage.
But what flows in electricity? Charges!
How do we measure this flow? By Current:
current = I = Dq / Dt
UNITS:
Amp(ere) = Coulomb / second
The rate at which electrons move along field lines
is called drift speed, typically about 10-4 m/s
Electric current defined in
terms of the flow of positive
charge opposite the
electrons is called
conventional current
Current will always be in the
same direction as the local
electric field
Voltage Sources
A battery or power supply supplies voltage. This is
analogous to what a pump does in a water system.
Question: Does a water pump supply water? If you
bought a water pump, and then plugged it in
(without any other connections), would water come
out of the pump?
Question: Does the battery or power supply actually
supply the charges that will flow through the
circuit?
*Charges move from
higher to lower
potential
*For the process to
continue, charges that
have moved from a
higher to lower
potential must be
raised back to a higher
potential again
*A battery is able to add
charges and raise the
charges to higher
electric potential
Symbol for a battery
*
Just like a water pump only pushes water (gives
energy to the water by raising the pressure of the
water), so the voltage source only pushes the
charges (gives energy to the charges by raising the
voltage of the charges).
Just like a pump needs water coming into it in order
to pump water out, so the voltage source needs
charges coming into it (into the negative terminal) in
order to “pump” them out (of the positive terminal).
*
Because of the “pumping” nature of voltage
sources, we need to have a complete circuit before
we have a current.
Circuit Elements
two of the common circuit elements:
capacitor
resistor
The capacitor is an element that stores charge for use
later (like a water tower).
The resistor is an element that “resists” the flow of
electricity.
Electrical Resistance
&
Ohms’ Law
The current established is directly proportional to the voltage
difference
Ohm’s Law: ΔV ∝ I
In a plot of ΔV vs I,
the slope is called the electrical resistance
Resistance
Current is somewhat like fluid flow. Recall that it took a
pressure difference to make the fluid flow due to the
viscosity of the fluid and the size (area and length) of the
pipe. So to in electricity, it takes a voltage difference to
make electric current flow due to the resistance in the
circuit.
By experiment we find that if we increase the voltage, we
increase the current: V is proportional to I. The constant
of proportionality we call the resistance, R:
V = I*R
Ohm’s Law
UNITS: R = V/I so Ohm = Volt / Amp.
The symbol for resistance is
Just as with fluid flow, the amount of resistance does not
depend on the voltage (pressure) or the current (volume
flow). The formula V=IR relates voltage to current. If
you double the voltage, you will double the current, not
change the resistance. The same applied to
capacitance: the capacitance did not depend
on the charge and voltage - the capacitance
related the two.
As was the case in fluid flow and capacitance,
the amount of resistance depends on the materials and
shapes of the wires.
The resistance depends on material and geometry (shape).
For a wire, we have:
R=rL/A
where r is called the resistivity (in Ohm-m) and measures
how hard it is for current to flow through the material, L
is the length of the wire, and A is the cross-sectional area
of the wire. The second lab experiment deals
with Ohm’s Law and the above equation.
*Electrical Power
The electrical potential energy of a charge is:
U = q*V .
Power is the change in energy with respect to time:
Power = DU / Dt .
Putting these two concepts together we have:
Power = D(qV) / Dt = V(Dq) / Dt = I*V.
Besides this basic equation for power:
P = I*V
remember we also have Ohm’s Law:
V = I*R .
Thus we can write the following equations for power:
P = I2*R = V2/R = I*V .
To see which one gives the most insight, we need to
understand what is being held constant.
Electrical Power and Electrical Work:
All electrical circuits have three parts in common.
*A voltage source.
*An electrical device
*Conducting wires.
The work done (W) by a voltage source is equal to the
work done by the electrical field in an electrical device,
Work = Power x Time.
electrical work is measured in joules
A joule/second is a unit of power called the watt.
Power = current x potential
Or,
P=IV
*Example
When using batteries, the battery keeps the voltage
constant. Each D cell battery supplies 1.5 volts, so four D
cell batteries in series (one after the other) will supply a
constant 6 volts.
When used with four D cell batteries, a light bulb is
designed to use 5 Watts of power. What is the resistance
of the light bulb?
*
We know V = 6 volts, and P = 5 Watts; we’re looking for R.
We have two equations:
P = I*V and V = I*R
which together have 4 quantities:
P, I, V & R..
We know two of these (P & V), so we should be able to
solve for the other two.
*
Using the power equation we can solve for I:
P = I*V, so 5 Watts = I * (6 volts), or
I = 5 Watts / 6 volts = 0.833 amps.
Now we can use Ohm’s Law to solve for R:
V = I*R, so
R = V/I = 6 volts / 0.833 amps = 7.2 W .
*Example extended
If we wanted a higher power light bulb, should we have a
bigger resistance or a smaller resistance for the light
bulb?
We have two relations for power that involve
resistance:
P=I*V; V=I*R; eliminating V gives: P = I2*R and
P=I*V; I=V/R; eliminating I gives: P = V2 / R .
In the first case, Power goes up as R goes up;
in the second case, Power goes down as R
goes up.
Which one do we use to answer the above
question?
*
In this case, the voltage is being held
constant due to the nature of the batteries.
This means that the current will change as
we change the resistance. Thus, the
P = V2 / R would be the most straight-forward
equation to use. This means that as R goes
down, P goes up. (If we had used the P = I2*R
Answer:
formula, as R goes up, I would decrease – so it would
not be clear what happened to power.)
The answer: for more power, lower the resistance. This
will allow more current to flow at the same voltage, and
hence allow more power!
*Kirchhoff’s Laws
* Junction Law:
at a junction in a circuit, the sum of the
current entering the junction will equal the sum of the
current leaving.
ΣI= ΣI
in
* Loop Law:
out
the sum of the potential drops around any
closed loop must add to
ΣV= 0
loop
*Connecting Resistors
There are two basic ways of connecting two resistors:
series and parallel.
In series, we connect resistors together like railroad cars;
this is just like we have for capacitors:
+
-
high V
+
-
low V
R1
R2
*
Series
To see how resistors combine to give an effective resistance
when in series, we can look either at
V = I*R,
or at
I
R = rL/A .
Vbat
+
-
R1
V1 V
2
R2
*
Series
Using V = I*R, we see that in series the current must move
through both resistors.
(Think of water flowing down two water falls in
series.) Thus Itotal = I1 = I2 .
Also, the voltage drop across the two resistors add to give
the total voltage drop:
(The total height that the water fell is the addition of
the two heights of the falls.)
Vtotal = (V1 + V2). Thus, Reff = Vtotal / Itotal =
(V1 + V2)/Itotal = V1/I1 + V2/I2 = R1 + R2.
*
Series
Using R = rL/A , we see that we have to go over both
lengths, so the lengths should add. The distances are in
the numerator, and so the values should add.
This is just like in R = V/I (from
add and are in the numerator!
V = IR) where the V’s
Note: this is the opposite of capacitors when connected
in series! Recall that
C = Q/V, where V is in the denominator!
*
Parallel
The result for the effective resistance for a parallel
connection is different, but we can start from the same
two places:
(Think of water in a river that splits with some
water flowing over one fall and the rest
falling over the other but all the water
ending up joining back together again.) V=I*R,
or R = rL/A .
Itotal
R2
+
Vbat
I1
-
R1 I2
*
Parallel
V=I*R, or R = rL/A
For parallel, both resistors are across the same
voltage, so Vtotal = V1 = V2 . The current can
go through either resistor, so: Itotal = (I1 + I2 )
.
Since the I’s are in the denominator, we have:
R = Vtotal/Itotal = Vtotal/(I1+I2); or
1/Reff = (I1+I2)/Vtotal = I1/V1 + I2/V2 = 1/R1 + 1/R2.
Parallel
If we start from R = rL/A , we can see that parallel
resistors are equivalent to one resistor with more Area.
But A is in the denominator (just like I was in the previous
slide), so we need to add the inverses:
1/Reff = 1/R1 + 1/R2 .
*Terminal Voltage
Terminal voltage, VT , is the potential difference between the
terminals of a battery.
Ideal voltage, VB , is determined by the chemistry of the battery.
Internal resistance, ir : some charge will be los due to the
random thermal motion of the battery
Terminal voltage will be:
VT = VB - ir
For recharging a battery:
VT = VB + ir
*Current Division
When current enters a junction, Kirchhoff’s first law tells you the
sum of the current entering must equal the sum of the current
leaving.
Example:
8 = I + 4I + 5I  I = 0.8 A
1/RP = 1/20 +1/5 +1/4 = ½  RP = 2Ω
V = IRP = 8 • 2 = 16V
16 = I1(20)  I1 = 0.8A
16 = I2(5)  I2 = 3.2A
16 = I3(4)  I3 = 4A
VB = 60 – 18 = 42V
1/RP = 1/12 + 1/6 = ¼  RP = 4Ω
Requiv = 4 + 8 + 6 + 3 = 21Ω
42 – I(21) = 0  I = 2A
VT60 = 60 – 2 • 1 = 58V
VT18 = 18 – 2 • 2 = 22V
2 = I + 2I  I = 0.67A
*
We define capacitance as the amount of charge stored per
volt: C = Qstored / DV.
UNITS:
Farad = Coulomb / Volt
Just as the capacity of a water tower depends on the size
and shape, so the capacitance of a capacitor depends on
its size and shape. Just as a big water tower can contain
more water per foot (or per unit pressure), so a big
capacitor can store more charge per volt.
*Parallel Plate Capacitor
For a parallel plate capacitor, we can pull charge from one
plate (leaving a -Q on that plate) and deposit it on
the other plate (leaving a +Q on that plate).
Because of the charge separation, we have a voltage
difference between the plates, DV. The harder we pull
(the more voltage across the two plates), the
more charge we pull: C = Q /DV. Note that C is NOT
CHANGED by either Q or DV; C relates Q and DV!
*
* What happens when a water tower is over-filled?
It can
break due to the pressure of the water pushing on the
walls.
* What happens when an electric capacitor is “over-filled”
or equivalently a higher voltage is placed across the
capacitor than the listed maximum voltage? It will
“break” by having the charge “escape”. This escaping
charge is like lightning - a spark that usually destroys the
capacitor.
*V or DV ?
When we deal with height, h, we usually refer to the
change in height, Dh, between the base and the top.
Sometimes we do refer to the height as measured from
some reference point. It is usually clear from the context
whether h refers to an actual h or a Dh.
With voltage, the same thing applies. We often just use V
to really mean DV. You should be able to determine
whether we really mean V or DV when we say V.
*
For this parallel plate capacitor, the capacitance is related
to charge and voltage (C = Q/V), but the actual
capacitance depends on the size and shape:
C plate ∝ A / d
A is the area of each plate, d is the distance between the
plates
*Energy Storage
If a capacitor stores charge and carries voltage, it also
stores the energy it took to separate the charge. The
formula for this is:
Estored = (1/2)QV = (1/2)CV2 ,
where in the second equation we have used the relation:
C = Q/V .
*
Note that previously we had:
U = q*V ,
and now for a capacitor we have:
Ucap = ½ QV = ½ CV2 = ½ Q2/C
*
The reason is that in charging a capacitor, the first bit of
charge is transferred while there is very little voltage on
the capacitor (recall that the charge separation creates
the voltage!). Only the last bit of charge is moved across
the full voltage. Thus, on average, the full charge
moves across only half the voltage!
*Hooking Capacitors
Together
Instead of making and storing all sizes of capacitors, we can
make and store just certain values of capacitors. When
we need a non-standard size capacitor, we can make it by
hooking two or more standard size capacitors together to
make an effective capacitor of the value we need.
*Two basic ways
There are two basic ways of connecting two capacitors:
series and parallel.
In series, we connect capacitors together like railroad cars;
using parallel plate capacitors it would look like this:
+
-
+
high V
-
low V
C1
C2
*Series
If we include a battery as the voltage source, the series
circuit would look like this:
C1
+
Vbat
C2
Note that there is only one way around the circuit, and you
have to jump BOTH capacitors in making the circuit - no
choice!
*Parallel
In a parallel hook-up, there is a branch point that allows
you to complete the circuit by jumping over either one
capacitor or the other: you have a choice!
High V
C1
C2
Low V
*
If we include a battery, the parallel circuit would look like
this:
+
Vbat
+
+
C1
C2
To see how capacitors combine to give an effective
capacitance when in series, we can look either at C =
Q/V, or at
C plate = A /d
*Formula for Series:
*
Using C = Q/V, we see that in series the charge moved
from capacitor 2’s negative plate must be moved through
the battery to capacitor 1’s positive plate.
C1
+
+Q
Vbat
C2
-Q
-
(  +Qtotal)
*
But the positive charge on the left plate of C1
will attract a negative charge on the right
plate, and the negative charge on the bottom
plate of C2 will attract a positive charge on
the top plate - just what is needed to give
the negative charge on the right plate of C1.
Thus Qtotal = Q1 = Q2 .
(+Q1  )
C1
+
+Q1
-Q 1
+Q2
Vbat
C2
-Q2
-
(  +Qtotal)
*
Also, the voltage drop across the two capacitors add to give
the total voltage drop:
Vtotal = (V1 + V2).
Thus, Ceff = Qtotal / Vtotal =
(with Qtotal = Q1 = Q2)
[1/Ceff] =
Qtotal / (V1 + V2),
or
(V1 + V2) / Qtotal = V1/Q1 + V2/Q2 =
1/C1 + 1/C2 = 1/Ceffective
*
For parallel, both plates are across the same
voltage, so Vtotal = V1 = V2 . The charge can
accumulate on either plate, so:
Qtotal = (Q1 + Q2).
Since the Q’s are in the numerator, we have:
Ceff = C1 + C2.
+
Vbat
+Q1
C1
-Q1
+Q2
C2
+Q1 
 +Qtotal = (Q1+Q2)
 +Q2
-Q2
Review of Formulas
Electric Current
I= ΔQ/Δt
Resistor Voltage Drop
V = IR
Resistivity
R = rL/A
Electric Power
P = IV
Resistance Power
P = I2R = V2/R
Junction Law
SI = SI
in
Loop Law
out
SΔV = 0
loop
Series Resistors
Rs = R1 + R2 +…
Parallel Resistors
1/RP = 1/R1 + 1/R2 +…
Terminal Voltage
VT = VB ± IR
Capacitance
C = Q/V
Parallel Plate Capacitor
C plate ∝ A / d
Capacitors in Series
1/Cs = 1/C1 + 1/C2 +…
Capacitors in Parallel
CP = C1 + C2 +…
Energy in Capacitor
U = ½ Q2 /C = ½ CV2 = ½ QV
Magnetism
Magnetic Fields:
A magnet that is moved in space near a second magnet
experiences a magnetic field.
A magnetic field can be represented by field lines.
The strength of the magnetic field is greater where the
lines are closer together and weaker where they are
farther apart.
Electric Currents
and
Magnetism
Oersted discovered that a compass
needle below a wire
(A) pointed north when there was
not a current,
(B) moved at right angles when a
current flowed one way, and
(C) moved at right angles in the
opposite direction when the
current was reversed.
A magnetic compass
shows the presence
and direction of the
magnetic field
around a straight
length of currentcarrying wire.
When a current is run
through a cylindrical
coil of wire, a
solenoid, it produces
a magnetic field like
the magnetic field of a
bar magnet. The
solenoid is known as
electromagnet.
Electric Meters:
*The strength of the magnetic
field produced by an
electromagnet is proportional to
the electric current in the
electromagnet.
*A galvanometer measures
electrical current by measuring
the magnetic field.
*A galvanometer can measure
current, potential difference, and
resistance.
Electric Motors:
*An electrical motor is an electromagnetic device
that converts electrical energy into mechanical
energy.
*A motor has two working parts - a stationary
magnet called a field magnet and a cylindrical,
movable electromagnet called an armature.
*The armature is on an axle and rotates in the
magnetic field of the field magnet.
*The axle is used to do work.