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ELECTRICITY & MAGNETISM (Fall 2011)
LECTURE # 12
BY
MOEEN GHIYAS
TODAY’S LESSON
(Series Circuit – Chapter 5)
Introductory Circuit Analysis by Boylested (10th Edition)
Today’s Lesson Contents
• Notation
• Internal Resistance of Voltage Sources
• Voltage Regulation
• Measurement Techniques
• Applications
• Solution to Problems
Notation – Voltage Sources and Ground
• Three ways to sketch the same series dc circuit
• If two grounds exist in a circuit and no connection
is shown between them, even then such a
connection exists for the continuous flow of charge.
Notation – Voltage Sources and Ground
• On large schematics
where space is at a
premium and clarity is
important, voltage
sources may be
indicated as in fig (a)
rather than as
illustrated in fig (b)
Notation – Voltage Sources and Ground
• On large schematics where space is at a premium and
clarity is important, voltage sources may be indicated
as fig (a) rather than as illustrated in fig (b)
Notation – Voltage Sources and Ground
• In schematics, the potential
levels may also be indicated
to permit a rapid check of the
potential levels at various
points in a network with
respect to ground to ensure
that the system is operating
properly
Notation – Double-Subscript Notation
• Voltage is an across variable and exists between two
points resulting in a double-subscript notation
• In fig, since a is the first subscript for Vab, point a must
have a higher potential than point b if Vab = +ve value.
• If point b is at a higher potential than point a, then
Vab = -ve value.
Notation – Single-Subscript Notation
• The single-subscript notation Va specifies the voltage at
point a with respect to ground (zero volts). Thus for
voltage at point b w.r.t to ground, we have Vb
• If the voltage is less than zero volts, a negative sign
must be associated with the magnitude of Va
Notation – General Comments
• Also the voltage Vab can be determined using
Eq. Vab = Va – Vb
• For fig below:
Notation
• Example – Find the voltage Vab for the conditions of fig
• Solution:
• Note the negative sign to reflect the fact that point b is
at a higher potential than point a.
Notation
• Example – Find voltage Va for the configuration of Fig
• Solution:
Notation
• Example – Find the voltage Vab for the configuration.
• Solution:
Notation & Voltage Divider Rule
• Example – Using the voltage divider rule, determine
the voltages V1 and V2 of fig.
• Solution: Circuit Redrawn,
• . From
• . voltage divider rule,
Notation & Voltage Divider Rule
• Example – For the network of fig
a) Calculate Vab.
b) Determine Vb.
c) Calculate Vc.
Notation & Voltage Divider Rule
a) Calculate Vab.
Solution:
c) Determine Vc.
Solution:
Notation & Voltage Divider Rule
b) Determine Vb.
• Solution:
• or
Internal Resistance of Voltage Sources
• Every voltage source, whether a generator, battery, or
laboratory supply (fig (a)) has some internal resistance.
• The equivalent circuit of any voltage source appears as
shown in fig (b).
Internal Resistance of Voltage Sources
• The effect of the internal resistance on the output
voltage is important to study in order to understand
unexpected changes in terminal characteristics of
voltage source.
Internal Resistance of Voltage Sources
• The ideal voltage source has no internal resistance and
an output voltage of E volts with no load or full load as
shown in fig (a).
Internal Resistance of Voltage Sources
• In the practical case [fig(b)], where we consider the
effects of the internal resistance, the output voltage will
be E volts only when no-load (IL = 0) conditions exist.
Internal Resistance of Voltage Sources
• When a load is connected [fig (c)], the output voltage of
the voltage source will decrease due to the voltage drop
across the internal resistance.
Internal Resistance of Voltage Sources
• By applying Kirchhoff’s voltage law around the indicated
loop of fig (c), we obtain
• Since
• We have
• And we get an important relation
• If Rint is not known, it can be found
Internal Resistance of Voltage Sources
• A direct consequence of the loss in output voltage is a
loss in power delivered to the load.
• Multiplying both sides of eq.
by the current IL in the circuit, we obtain
Internal Resistance of Voltage Sources
• For a dc generator, a plot of the output voltage versus
current appears in fig
Internal Resistance of Voltage Sources
• Note that any increase in load demand causes a drop
in terminal voltage due to the increasing loss in
potential across the internal resistance.
Internal Resistance of Voltage Sources
• At maximum current IFL, the voltage across the internal
resistance is Vint = IFLRint = (10 A)(2 ) = 20 V, and the
terminal voltage has dropped to 100 V—a significant
difference (from 120V) even if you stay below the listed
full-load current.
Internal Resistance of Voltage Sources
• Eventually, if the load current were permitted to
increase without limit, the voltage across the internal
resistance would equal the supply voltage, and the
terminal voltage would be zero.
Internal Resistance of Voltage Sources
• The larger the internal resistance, the steeper is the
slope of the characteristics of fig
• In fact, for any chosen interval of voltage or current, the
magnitude of the internal resistance is given by
Internal Resistance of Voltage Sources
• Example – Before a load is applied, the terminal voltage
of the power supply of is set to 40V. When a load of
500Ω is attached, the terminal voltage drops to 38.5 V.
What happened to the remainder of the no-load voltage,
and what is the internal resistance of the source?
Internal Resistance of Voltage Sources
• Solution:
• The difference of 40 V – 38.5 V = 1.5 V now appears
across the internal resistance of the source.
• The load current IL = 38.5 V/0.5 kΩ = 77 mA.
• . Applying Eq.
38.5V38.5V
Internal Resistance of Voltage Sources
• Example – The battery of fig has an internal resistance
of 2Ω . Find the voltage VL and the power lost to the
internal resistance if the applied load is a 13Ω resistor.
• Solution:
Voltage Regulation
• If a supply is set for 12 V, it is desirable that it maintain
this terminal voltage, even though the current demand
on the supply may vary.
• A measure of how close a supply will come to ideal
conditions is given by the voltage regulation
characteristic.
Voltage Regulation
• By definition, the voltage regulation (VR) of a supply
between the limits of full-load and no-load conditions
(Fig. 5.56) is given by the following:
Voltage Regulation
• We see for ideal conditions, VFL = VNL and VR% = 0.
• Therefore, the smaller the voltage regulation, the less
the variation in terminal voltage with change in load.
• It can be shown with a short derivation that the voltage
regulation is also given by
• The smaller the internal resistance for the same load,
the smaller the regulation and more ideal the output.
Voltage Regulation
• Example - Calculate the voltage regulation of a supply
having the characteristics of Fig. 5.53.
• Solution:
Voltage Regulation
• Example - Determine the voltage regulation of the
supply of fig with internal resistance of 19.48Ω and
load resistance as 500Ω.
• Solution:
38.5V38.5V
Measurement Techniques - Ammeters
• Ammeters are placed in series with the branch in which
the current is to be measured
• For minimal impact on the network behaviour,
ammeter’s resistance should be very small (ideally zero
ohms) compared to the other series elements of the
branch
Measurement Techniques - Ammeters
• If the meter resistance approaches or exceeds 10% of
branch resistance R, it will have a significant impact
on the current level it is measuring.
• It is also noteworthy that the resistances of the
separate current scales of the same meter are usually
not the same.
• In fact, the meter resistance normally increases with
decreasing current levels.
Measurement Techniques - Ammeters
• For an up-scale (analog meter)
or positive (digital meter)
reading, an ammeter must be
connected with current entering
the positive terminal (Red) of
the meter and leaving the
negative terminal (Black), as
shown in fig.
Measurement Techniques - Voltmeters
• Voltmeters are always hooked up across
the element for which the voltage is to
be determined.
• An up-scale or positive reading on a
voltmeter is obtained by connecting
positive terminal (red lead) to the point
of higher potential and the negative
terminal (black lead) is connected to the
lower potential
Measurement Techniques - Voltmeters
Measurement Techniques - Voltmeters
• The internal resistance of a supply cannot be
measured with an ohmmeter due to the voltage
present.
Measurement Techniques - Voltmeters
• However, the no-load voltage can be measured by
simply hooking up the voltmeter as shown.
• The internal resistance of the voltmeter is usually
sufficiently high to ensure that the resulting current is
so small that it can be ignored.
Measurement Techniques
• It seems we can find by Ohm’s law: Rint = ENL /ISC.
• However, Rint of the voltage supply may be very low,
resulting in high current levels which could damage the
ammeter and supply.
• A better approach would be to apply a RL resistive load
and then measure current and use following eq. To
calculate Rint.
Applications – Holiday Lights
• If one wire enters and leaves the bulb casing, they are
in series.
• If two wires enter and leave, they are probably in
parallel.
Applications – Holiday Lights
• When bulbs are connected in series, if one burns out
(the filament breaks and circuit opens), and all the
bulbs should go out
Applications – Holiday Lights
• However, the holiday bulbs are specially designed to
permit current to continue to flow to the other bulbs
when the filament burns out.
• Note that only one flasher unit is required per 50 bulb
panel
Applications – Holiday Lights
• The bulbs of fig are rated 2.5 V at 0.2 A or 200 mA.
• Since there are 50 bulbs in series, the total voltage will
be 50 x 2.5 V = 125 V which matches voltage available
• Since the bulbs are in series, the current through each
bulb will be 200 mA.
• The power rating of each bulb is therefore P = VI (2.5
V)(0.2 A) = 0.5 W with a total wattage demand of
50 x 0.5 W = 25 W.
Applications – Holiday Lights
• When each set is connected together, they will actually
be in parallel
• Note that the top line is the hot line to all the connected
sets, and the bottom line is the return, neutral, or
ground line for all the sets.
Applications - Microwave
Solution to Problems
• #24a – Determine the voltages Va, Vb, and Vab for the
network
• Solution:
Va = 12 - 8 = 4V
Vb = -8V
Vab = 12V
Solution to Problems
• #32b – Find the voltage VL and the power loss in the
internal resistance for the configuration of fig
• Solution:
IL = 12 / (0.05+3.3)
= 12 / 3.35 = 3.58 A
VL = E – IL Rint = 12 – 3.58 x 0.05
= 12 – 0.179 = 11.82 V
Summary / Conclusion
• Notation
• Internal Resistance of Voltage Sources
• Voltage Regulation
• Measurement Techniques
• Applications
• Solution to Problems