Investigatory project

1. CERTIFICATE
This is to certify that this dissertation is a
bonafide record of the project work done by
______________ of class XII
(science) REG NO.______________ under my
guidance and supervision in partialfulfillment of
the requirements for appearing in AISSCE
March 2014Principal Teacher in ChargeExternal
Examiner No____________

2. Internal resistance
1. Internal Resistance, EMF and
Oscilloscopes
 2. What we are going to achieve today
o Creating power from lemons
o Find out about internal resistance of
batteries
o Know what is the electromotive force is
o Use an oscilloscope to measure the
frequency and voltage from an signal
generator
 3. Using lemons, limes and potatoes to
power an LED zinc copper
 4. Making Batteries There is nothing
special about batteries – but these have a
high internal resistance. R l What do you
think the best way to minimise the internal

3. resistance of your battery? Think about
resistivity (lemon is a poor conductor)
 5. Batteries What is the main energy
transfer in a battery? Electrical energy
This is powered by two 1.5 V AA cells in
series - what is the supply voltage? What
is the emf of the supply? After a while the
battery needs to be replaced; why? What
determines how quickly it runs down?
What determines how much current is
drawn from the supply?
 6. EMF Electromotive Force
EMF is the external work expended per unit
of charge to produce an electric potential
difference across two open-circuited terminals
o This is the same definition as voltage but on
an open circuit (no current flow)
o Why is this definition important?

4.  7. Batteries have internal resistance The
circuit now has two resistors in The
internal resistance of the battery, r is very
small. R is much larger The total
resistance of this circuit is R total = R +r I
= E / (R+r)
 8. Batteries have internal resistance As
charge goes around the circuit the sum of
emfs must equal the sum of voltage drops
leading to EMF = I R + I r The terminal
voltage is equal to I R so this can be
rearranged to give: V = E – I r and
interpreted as terminal voltage = emf –
‘lost volts’
 9. R -small R total = r + R -small The
current will now be larger as the total
resistance of the circuit is much lower The
voltage lost across r V = I (large) r The
voltage lost will now be a problem This
case is of a small load resistance
connected to a battery is seen in a starter
motor on a car

5.  10. Starter motor on a conventional car
The headlamps are connected in parallel
across a twelve-volt battery. The starter
motor is also in parallel controlled by the
ignition switch. Since the starter motor
has a very low resistance it demands a
very high current (say 60 A). The battery
itself has a low internal resistance (say
0.01 Ω). The headlamps themselves draw
a much lower current (they have a higher
resistance) Lamp R Starter motor Ignition
switch 12V What will happen to the
lights?
 11. A use of high internal resistance
 12. Quick Questions
o .1. A 9.0 V battery has an internal
resistance of 12.0
o (a) What is the potential difference across
its terminals when it is supplying a current
of 50.0 mA?

6. o What is the maximum current this battery
could supply?
o Draw a sketch graph to show how the
terminal potential difference varies with the
current supplied if the internal resistance
remains constant. How could the internal
resistance be obtained from the graph?
o and the current rises to 60 mA. What is the
emf and internal resistance of the cell? .
When the wearer turns up the volume, the
resistance is changed to 100 2. A cell in a
deaf aid supplies a current of 25.0 mA
through a resistance of 400
V = E – I r V = IR E = I(R +r) You need to
set up a simultaneous equation
 13. E = 10 + (25 x 10 -3 x 114.3) = 12.86
V I VAnswers 1. (a) pd = E – I r = 9 –
(50 x 10 -3 x 12) = 8.4 V (b) Max current
= E/r = 9 / 12 = 0.75 A 2. E = I(R +r) E =
25 x 10 -3 (400 + r) and E = 60 x 10 -3

7. (100 + r) So 25 x 10 -3 (400 + r) = 60 x 10
-3 (100 + r) so r = 114.3
 14. Oscilloscope Use the signal generator
to create A/C (alternating current) on the
Oscilloscope Draw 2 signals of 2 different
frequencies Work out the frequency of the
Oscilloscope Add the magnitude of the
wave height How do you use an
oscilloscope as a dc and ac voltmeter?
How do you use it to measure frequency?
 15. Voltage what the average value of an
ac voltage or current is over a whole
number of cycles? power is calculated by
P = IV , both I and V change sign
together, so power is always positive
 16. Positive power calling the maximum
value of I p V p and a minimum of zero
0V P = I p V p Average power = ½ I p V
p P = 1/2 I p V p = 1/2 I p 2 R = 1/2
V p 2 / R (using V = I R)

8.  17. RMS voltage (root mean squared)
RMS links the dc equivalent values to ac
peak values. The point is that a sinusoidal
ac supply of peak value V p delivers the
same average power as steady dc of
value V p / √2 The same power would be
delivered by a dc with values I and V if:
P = I 2 R= 1/2 I p 2 R
and P = V 2 / R = 1/2 V p 2
/ R I 2 R= 1/2 I p 2 R (divide both
sides by R) V 2 / R = 1/2 V p 2 / R
(multiply by R) These lead to the
equations: I 2 = I p 2 / 2 V 2 = V p
2 / 2 (square root) I = I p / √2 V = V
p / √2
 18. RMS Graph listed voltages for power
outlets, e.g. 120 V (USA) or 230 V
(Europe), are almost always quoted in
RMS values, and not peak values
 19. Questions

9. o 1. The mains ac supply in some countries is
110 V r.m.s at 50 Hz (sinusoidal).
o (a) What is the peak value of voltage?
o (b) What is the peak-to-peak value of
voltage?
o (c) How long does one cycle of this ac
supply last?
o (d) A 100 W lamp is designed for use with
110 V ac What is the resistance of its
filament? (use r.m.s. value for V)
o 2. Which will light a lamp more brightly, 12
V peak ac or 12 V steady dc? Explain.
o UK mains ac has an r.m.s. value of 230 V
and a frequency of 50 Hz. Sketch a graph of
voltage against time for one cycle of this ac
and include values for peak voltage and
time period on the axes.

10. o What is the ratio of powers delivered by 20
V dc and 20 V peak ac to the same load?
V p =r.m.s x √ 2 Wavelength = 1 /
frequency
 20. 2. 12 V peak ac is equivalent to 12/√
2 V = 8.5 V dc equivalent. So 12 V peak
to peak is dimmer. 3. 230 x √ 2 V = 325V,
so graph varies between + 325 V and -
325 V. One time period = 1 / 50 Hz =
0.02s 4. P = V 2 /R so the ratio of powers
is ratio of voltages squared. 20 V peak ac
is equivalent to 20/ √ 2 V dc i.e. 14.14 V
so dc power / ac power = 20 2 /14.14 2 =
2 or dc V 2 / (ac peak / √ 2) 2 = (√ 2) 2
=2Answers and Worked Solutions 1. (a)
110 x √ 2 = 155.6 V (b) 2 x 155.6 = 311 V
(c) 1 / 50 Hz = 0.02s (d) P = V 2 /R R =
12100/100 = 121

12. Current electricity
1. K V, NAL CAMPUS, B’LORE •
CURRENT ELECTRICIY
 2. 1. Electric Current 2. Conventional
Current 3. Drift Velocity of electrons
and current 4. Current Density 5.
Ohm’s Law 6. Resistance, Resistivity,
Conductance & Conductivity 7.
Temperature dependence of resistance
8. Colour Codes for Carbon Resistors
9. Series and Parallel combination of
resistors 10. EMF and Potential
Difference of a cell 11. Internal
Resistance of a cell 12. Series and
Parallel combination of cells
 3. Electric Current: The electric current
is defined as the charge flowing
through any section of the conductor in

13. one second. I = q / t (if the rate of flow
of charge is steady) I = dq / dt (if the
rate of flow of charge varies with time)
Different types of current: I t 0 a b c d)
Alternating current whose magnitude
varies continuously and direction
changes periodically a) Steady current
which does not vary with time b) & c)
Varying current whose magnitude
varies with time d
 4. Conventional Current: Conventional
current is the current whose direction is
along the direction of the motion of
positive charge under the action of
electric field. + + + + - - - - + + + + - - - -
I Drift Velocity and Current: Drift
velocity is defined as the velocity with
which the free electrons get drifted
towards the positive terminal under the
effect of the applied electric field. Ivd = -
(eE / m) τ - - -vd E l A I = neA vdvd = a

14. τ vd - drift velocity, a – acceleration, τ –
relaxation time, E – electric field, e –
electronic charge, m – mass of
electron, n – number density of
electrons, l – length of the conductor
and A – Area of cross-section Current
is directly proportional to drift velocity.
Conventional current due to motion of
electrons is in the direction opposite to
that of motion of electrons. + + + I - - -
 5. Current density: Current density at a
point, within a conductor, is the current
through a unit area of the conductor,
around that point, provided the area is
perpendicular to the direction of flow of
current at that point. J = I / A = nevd In
vector form, I = J . A Ohm’s Law: The
electric current flowing through a
conductor is directly proportional to the
potential difference across the two ends
of the conductor when physical

15. conditions such as temperature,
mechanical strain, etc. remain the
same. I V I α V or V α I or V = R I V I 0
 6. Resistance: The resistance of
conductor is the opposition offered by
the conductor to the flow of electric
current through it. R = V / I Resistance
in terms of physical features of the
conductor: I = neA | vd | I = neA (e |E| /
m) τ ne2 Aτ m V l I = ne2 Aτ V I = ml
ne2 τ A R = m l A R = ρ l where ρ = ne2
τ m is resistivity or specific resistance
Resistance is directly proportional to
length and inversely proportional to
cross-sectional area of the conductor
and depends on nature of material.
Resistivity depends upon nature of
material and not on the geometrical
dimensions of the conductor.

16.  7. When temperature increases, vd
decreases and ρ increases. When l
increases, vd decreases. Relations
between vd , ρ, l, E, J and V: ρ = E / J =
E / nevd vd = E /(neρ) vd = V /(neρl)
(since, J = I / A = nevd ) (since, E = V / l
) Conductance and conductivity:
Conductance is the reciprocal of
resistance. Its S.I unit is mho.
Conductivity is the reciprocal of
resistivity. Its S.I unit is mho / m.
Temperature dependence of
Resistances: ne2 τ A R = m l When
temperature increases, the no. of
collisions increases due to more
internal energy and relaxation time
decreases. Therefore, Resistance
increases. Temperature coefficient of
Resistance: R0 t α = Rt – R0 R1t2 –
R2t1 α = R2 – R1 or R0 – Resistance
at 0°C Rt – Resistance at t°C R1 –
Resistance at t1°C R2 – Resistance at
t2°CIf R2 < R1, then α is – ve.

17.  8. Colour code for carbon resistors: B V
B Gold G R B Silver B V B The first two
rings from the end give the first two
significant figures of resistance in ohm.
The third ring indicates the decimal
multiplier. The last ring indicates the
tolerance in per cent about the
indicated value. Eg. AB x 10C ± D %
ohm 17 x 100 = 17 ± 5% Ω 52 x 106 ±
10% Ω 52 x 100 = 52 ± 20% Ω Letter
Colour Number Colour Tolerance B
Black 0 Gold 5% B Brown 1 Silver 10%
R Red 2 No colour 20% O Orange 3 Y
Yellow 4 G Green 5 B Blue 6 V Violet 7
G Grey 8 W White 9 B B ROY of Great
Britain has Very Good Wife
 9. Another Colour code for carbon
resistors: Yellow Body Blue Dot Gold
Ring YRB Gold 42 x 106 ± 5% Ω Red
Ends i) The colour of the body gives the
first significant figure. ii) The colour of

18. the ends gives the second significant
figure. iii) The colour of the dot gives
the decimal multipier. iv) The colour of
the ring gives the tolerance. Series
combination of resistors: Parallel
combination of resistors: R = R1 + R2 +
R3 R is greater than the greatest of
all.R1 R2 R3 R1 R2 R3 1/R =1/R1 +
1/R2 + 1/R3 R is smaller than the
smallest of all.
 10. Sources of emf: The electro motive
force is the maximum potential
difference between the two electrodes
of the cell when no current is drawn
from the cell. Comparison of EMF and
P.D: EMF Potential Difference 1 EMF is
the maximum potential difference
between the two electrodes of the cell
when no current is drawn from the cell
i.e. when the circuit is open. P.D is the
difference of potentials between any

19. two points in a closed circuit. 2 It is
independent of the resistance of the
circuit. It is proportional to the
resistance between the given points. 3
The term ‘emf’ is used only for the
source of emf. It is measured between
any two points of the circuit. 4 It is
greater than the potential difference
between any two points in a circuit.
However, p.d. is greater than emf when
the cell is being charged.
 11. Internal Resistance of a cell: The
opposition offered by the electrolyte of
the cell to the flow of electric current
through it is called the internal
resistance of the cell. Factors affecting
Internal Resistance of a cell: i) Larger
the separation between the electrodes
of the cell, more the length of the
electrolyte through which current has to
flow and consequently a higher value of

20. internal resistance. ii) Greater the
conductivity of the electrolyte, lesser is
the internal resistance of the cell. i.e.
internal resistance depends on the
nature of the electrolyte. iii) The internal
resistance of a cell is inversely
proportional to the common area of the
electrodes dipping in the electrolyte. iv)
The internal resistance of a cell
depends on the nature of the
electrodes. R rE II E = V + v = IR + Ir =
I (R + r) I = E / (R + r) This relation is
called circuit equation. V v
 12. Internal Resistance of a cell in
terms of E,V and R: R rE II V v E = V +
v = V + Ir Ir = E - V Dividing by IR = V,
Ir E – V = IR V E r = ( - 1) R V
Determination of Internal Resistance of
a cell by voltmeter method: r K R.B (R)
V + r II R.B (R) K V + Open circuit (No
current is drawn) EMF (E) is measured

21. Closed circuit (Current is drawn)
Potential Difference (V) is measured
 13. Cells in Series combination: Cells
are connected in series when they are
joined end to end so that the same
quantity of electricity must flow through
each cell. R II V rE rE rE NOTE: 1. The
emf of the battery is the sum of the
individual emfs 2. The current in each
cell is the same and is identical with the
current in the entire arrangement. 3.
The total internal resistance of the
battery is the sum of the individual
internal resistances. Total emf of the
battery = nE (for n no. of identical cells)
Total Internal resistance of the battery =
nr Total resistance of the circuit = nr +
R Current I = nE nr + R (i) If R << nr,
then I = E / r (ii) If nr << R, then I = n (E
/ R) Conclusion: When internal
resistance is negligible in comparison

22. to the external resistance, then the cells
are connected in series to get
maximum current.
 14. Cells in Parallel combination: Cells
are said to be connected in parallel
when they are joined positive to
positive and negative to negative such
that current is divided between the
cells. NOTE: 1. The emf of the battery
is the same as that of a single cell. 2.
The current in the external circuit is
divided equally among the cells. 3. The
reciprocal of the total internal
resistance is the sum of the reciprocals
of the individual internal resistances.
Total emf of the battery = E Total
Internal resistance of the battery = r / n
Total resistance of the circuit = (r / n) +
R Current I = nE nR + r (i) If R << r/n,
then I = n(E / r) (ii) If r/n << R, then I =
E / R Conclusion: When external

23. resistance is negligible in comparison
to the internal resistance, then the cells
are connected in parallel to get
maximum current. V R II rE rE rE

24. Inernal resistance
A practical electrical power source which is a
linear electric circuit may, according to Thévenin's
theorem, be represented as an ideal voltage
source in series with an impedance. This
resistance is termed theinternal resistance of the
source. When the power source delivers current,
the measured voltage output is lower than the no-
load voltage; the difference is the voltage drop
(the product of current and resistance) caused by
the internal resistance. The concept of internal
resistance applies to all kinds of electrical sources
and is useful for analyzing many types of
electrical circuits.
Batteries
Batteries can be approximately modeled as a
voltage source in series with a resistance. The
internal resistance of a battery is dependent on
the specific battery's size, chemical properties,
age, temperature and the discharge current. It has

25. an electronic component due to the resistivity of
the battery's component materials and an ionic
component due to electrochemical factors such as
electrolyte conductivity, ion mobility, and electrode
surface area. Measurement of the internal
resistance of a battery is a guide to its condition,
but may not apply at other than the test
conditions. Measurement with an alternating
current, typically at a frequency of 1kHz, may
underestimate the resistance, as the frequency
may be too high to take into account the slower
electrochemical processes. Internal resistance
depends upon temperature; for example, a
fresh Energizer E91 AA alkaline primary battery
drops from about 0.9 ohms at -40 °C, where the
low temperature reduces ion mobility, to about
0.15 ohms at room temperature and about 0.1
ohms at 40 °C.[1]

26. The internal resistance of a battery can be
calculated from its open circuit voltage, voltage
on-load, and the load resistance:
Many equivalent series resistance (ESR) meters,
essentially AC milliohmmeters normally used to
measure the ESR of capacitors, can be used to
estimate battery internal resistance, particularly to
check the state of discharge of a battery rather
than obtain an accurate dc value.[2]
Some
chargers for rechargeable batteries indicate the
ESR.
In use the voltage across the terminals of a
disposable battery driving a load decreases until it
drops too low to be useful; this is largely due to an
increase in internal resistance rather than a drop
in the voltage of the equivalent source.

27. With rechargeable lithium polymer batteries the
internal resistance is largely independent of the
state of charge, but increases as the battery ages,
thus is a good indicator of expected life.

28. EMF measurements are measurements of
ambient (surrounding) electromagnetic fields that
are performed using particular sensors or probes,
such as EMF meters. These probes can be
generally considered as antennas although with
different characteristics. In fact probes should not
perturb the electromagnetic field and must
prevent coupling and reflection as much as
possible in order to obtain precise results. There
are two main types of EMF measurements:
 broadband measurements performed using a
broadband probe, that is a device which senses
any signal across a wide range of frequencies
and is usually made with three independent
diode detectors;
 frequency selective measurements in which the
measurement system consists of a field
antenna and a frequency selective receiver or

29. spectrum analyzer allowing to monitor the
frequency range of interest.
EMF probes may respond to fields only on one
axis, or may be tri-axial, showing componets of
the field in three directions at once. Amplified,
active, probes can improve measurement
precision and sensitivity but their active
components may limit their speed of response.