The University of Reading
Department of Physics
Chapter 9
Project 1 Electricity
Experiment A: DC Networks
9A.1 Objectives
(i)
To understand the concept of
the Thevenin Equivalence and its
implications
for
electronic
instrumentation and circuitry.
(ii) To perform experiments with
DC networks.
open circuit voltage V, derive an
expression for the output Vout, from a
simple two-resistor (R1, R2) voltage
divider.
9A.4 Safety Procedures
9A.2 Prior Reading
Please
observe
the
standard
precautions associated with electrical
equipment.
Ohanian Chapters 28 and 29: FLAP
module P4.1.
9A.5 Introduction
9A.3 Preparatory Work
(i)
From Kirchoff’s Laws, show
that the equivalent resistance (R) of
three resistors in series (R1, R2, R3),
can be written:R = R1 + R2 + R3
(ii) From Kirchoff’s Laws, show
that the equivalent resistance (R) of
three resistors in parallel (R1, R2, R3),
can be written:1
1
1 1
= + +
R R1 R2 R3
(iii) Explain the term voltage
divider circuit.
(iv) If a voltage generator with
internal resistance R0 produces an
Experimental Physics
For a circuit containing only voltage
generators and resistors, Thevenin's
Theorem states that any combination
of voltage generators and resistors
considered at the terminals A and B
is equivalent at those terminals to a
single voltage generator, VTh, in
series with a single resistor, RTh. VTh
is equal to the open circuit voltage
between A and B, RTh is the
resistance that would be measured
between A and B if all the voltage
generators were replaced by short
circuits. The objective of this project
is to test this theorem.
9A.6 Background
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There are a number of basic rules
which may be used in all network
analysis. Resistors (R1, R2 .. etc)
connected in series may be replaced
by an equivalent resistance R:R = R1 + R2 + R3 + R4 ...
Similarly, for resistors connected in
parallel:1
1
1 1
= + + .....
R R1 R2 R3
These lead to the voltage divider
rule; the voltage across two
resistances connected in series
divides between them in the ratio of
their
resistances.
Resistances
connected in parallel act as a current
divider. These rules are effectively
specific cases of Kirchhoff's laws.
The first states that at any node in a
network, at every instant of time, the
algebraic sum of the currents at the
node is zero. (For this law, currents
entering a node are considered
positive, those directed out of the
node are negative). The second law
states that the algebraic sum of
voltages across all the components
around any loop of a circuit is zero.
These rules may be used to analyze
any specific circuit but is often useful
to exploit Thevenin's Theorem to
simplify the circuit and hence the
analysis.
9A.7 The Experiment
9A.7.1 The Internal Resistance
of the Power Supply
In this project you will first find the
Thevenin Equivalent quantities for a
"black box" in the form of a mains
powered variable DC voltage supply.
We do not ask about the circuit
inside the box, and hence VTh and RTh
must be determined experimentally.
You should set the output of the
voltage supply to ~6V. (If you
change the output before the very last
step you will need to start again
unless you know the setting
precisely).
Thevenin's Theorem states:As far as any load connected across its output terminals is
concerned, a linear circuit consisting of voltage sources,
current sources and resistances is equivalent to an ideal
voltage source VTh in series with a resistance RTh. The value
of the voltage source is equal to the open circuit voltage of
the linear circuit. The resistance is equal to the resistance
which would be measured between the output terminals if the
load was removed and all sources were replaced by their
internal resistances.
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the equipment! This factor sets a
minimum level for RL.
For a voltage generator it is usual to
call RTh the output resistance R0 and
VTh the output voltage, V (open
circuit). For this particular voltage
generator, the output resistance R0
depends on the voltage setting, so
that if this setting is altered, a new
value for R0 will have to be found.
9A.7.2 Thevenin’s Theorem and
the Voltage Divider Circuit
The open circuit voltage V between
the output terminals can be measured
directly using a multimeter, since the
meter has a very high resistance and
draws negligible current when in the
voltage mode.
RTh cannot be
measured
directly
using
a
multimeter. However, it may be
obtained indirectly by measuring the
current through various resistive
loads connected across the voltage
generator. You will need to derive
an expression which relates the
current to RTh and you will need to
decide how to plot the data usefully.
Use the resistance box as a variable
load.
Measure the current for
various loads RL and carry out your
analysis and hence find the value of
RTh.
The analysis of complicated
electrical networks may often be
simplified by the use of Thevenin's
theorem when VTh and RTh are
calculated theoretically.
In this
experiment, you will now evaluate
experimentally the behaviour of a
specific circuit and then set up the
Thevenin equivalent circuit to see if
it behaves in the same way.
The test circuit, shown below, is the
NB Ensure that you never exceed
the current carrying capabilities of
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voltage supply with a potential
divider across its output. Set up the
potential divider circuit as shown in
this figure. Determine the Thevenin’s
equivalents for this circuit using the
same procedure as above. When you
have completed these measurements
you will able to check the results by
calculation. If you measure the
resistances in the potential divider
you should be able to use the rules
described in Section 9A.6 and the VTh
and RTh for the voltage generator
theoretically to determine the
equivalents for the generator plus
divider.
How do the values
compare?
Experimental Physics
Now, before you dismantle your
circuit, you will need to decide how
you will determine whether that
circuit and the equivalent circuit
constructed using VTH and RTH have
the same properties. When you have
a plan, discuss it with a
demonstrator.
Carry out the
approved plan and construct the
equivalent Thevenin circuit shown in
the above figure. Remember that the
voltage generator has an internal
resistance and so you will need to
think carefully what value you
should set RTH to in your equivalent
circuit. Use the precision variable
resistance as RTH. Were the circuits
equivalent?
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Experiment B: Electrons and Semi-conductors
9B.1 Objectives
(a) To
investigate
the
current/voltage characteristics of a
semiconductor device.
(b) To analyze quantitatively its
exponential characteristics.
(c) To use the response to
measure temperature.
9B.2 Prior Reading
Ohanian Chapter 44.3-44.5: FLAP
module P11.4.
9B.3 Preparatory Work
(i)
Sketch the current voltage
characteristics of a diode.
(ii) Consider the characteristics of
the diode, as represented by the
equation given in Section 9B.5.
Explain what you understand by the
saturation current is and indicate this
on the above sketch.
(iii) Rearrange the equation given
in Section 9B.5 such that it can be
plotted as a straight-line graph,
assuming that is<<i.
(iv) How could this assumption be
tested experimentally?
9B.4 Safety Procedures
Liquid nitrogen is very cold and
prolonged contact will result in a
severe burn. This liquid must be
Experimental Physics
handled with extreme caution and
particular care must be taken to
avoid contact with your eyes.
Safety goggles must be worn at all
times!
9B.5 Introduction
Many electronic devices contain
semi-conducting materials such as
silicon, germanium and gallium
arsenide. In particular, junctions
between different semiconductors
(pn junctions, bipolar transistors),
semiconductors and insulators (field
effect
transistors),
and
semiconductors
and
metals
(Schottky
diodes)
are
often
employed to produce electronic
devices. In this experiment you will
study the behaviour of a simple
electronic component, namely a
silicon diode. By considering the
response of this device to various
applied voltages you will then be
able to use it to measure the
temperature of boiling liquid
nitrogen.
Most of the electronic components
that you have encountered obey
Ohm's Law. That is, the current, i,
that flows in the device is
proportional to the voltage, V, that is
applied to it:-
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i∝V
Examples of so-called linear devices
are resistors, capacitors and
inductors.
A diode is a device which will only
conduct electricity in one direction:
even in this, the forward direction,
the current is not proportional to the
voltage. A diode is therefore a nonlinear electronic device.
Diodes contain a junction between
two dissimilar materials, such as a
metal and a semiconductor, and
electrons move easily in one
direction but find it almost
impossible to move in the opposite
direction. A number of processes
may be involved at the junction, but
the net result is the injection of
electrons from one material into the
other when a suitable electric field is
applied. A suitable electric field
equals a voltage applied in the
forward direction: the injection of
electrons equals a current which
flows throughout the circuit. The
behaviour of such a device can be
analyzed using the following
empirical relationship:i = is [exp(
eV
) − 1]
nkT
Experimental Physics
In the above equation, V is the
applied voltage, i is the current that
flows at a temperature T, and e, k, is,
and n are constants; e is the charge
on an electron, k is the Boltzmann
constant, is is the saturation current
and n is an ideality factor which
equals one for an ideal diode but
which, in practice, is somewhat
higher.
9B.6 The Experiment
Set up the circuit shown below,
which will enable you to investigate
the current/voltage relationships of
the diode.
Because of the non-linear behaviour
of this device, before taking any
measurements, take a few minutes to
explore the way in which the current
varies with the applied voltage in
the forward direction. Be careful
not to exceed the maximum current
that the AVOmeter or the diode can
handle! The current should always
be less than 10mA.
Repeat the above with the diode
connected in the reverse direction.
What is the maximum current that
you can observe with the given
power supply? What happens if you
disconnect the voltmeter? Now, you
should be able to estimate the
magnitude of is.
Discuss your
conclusion with a demonstrator
before proceeding.
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once again, plot a graph on loglinear graph paper. From this you
can evaluate the temperature of the
diode, which will be very close to
that of the liquid nitrogen.
Now, returning to the forward
direction, take measurements of the
current as a function of applied
voltage and, by plotting a suitable
graph on log-linear graph paper,
evaluate the diode ideality factor, n.
Also, by replotting your data,
produce a better estimate of is. How
does this value compare with your
previous estimate and is the
approximation made in Section 9B.3
justified?
You are now in a position to use the
diode to measure temperature, since
you can measure i as a function of
V, and you know e, n and k.
Get a demonstrator to pour out some
liquid nitrogen for you and then
immerse the diode; leave it for a few
minutes to cool.
AVOmeter
D.C
Volts
Diode
Digital
Voltmeter
Take measurements of the current as
a function of applied voltage and,
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Notes: Project 1
Experimental Physics
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