Lecture 5 – DC Power and
circuits
Prof. Naomi Harte
DC Electric Sources
• DC sources refer to sources of electrical energy which are associated with
constant voltages and currents.
• A DC power supply can be constructed as an electronic circuit operating from
the ac mains electricity supply and designed to deliver a dc voltage and
current.
• An alternative DC source is the battery which is commonly used in portable
equipment and machines where a connection to the mains ac supply is not
convenient or practical.
• Ultracapacitors—capacitors of extremely high value—are being developed for
transportation, using a large capacitor to store DC energy instead of the
rechargeable battery banks used in hybrid vehicles
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DC?
• Direct Current
• Read all about DC and AC here:
• http://engineering.mit.edu/ask/what%E2%80%99s-
difference-between-ac-and-dc
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Batteries
• The DC battery is commonplace today. Batteries are used in
the widest range of scenarios, from the smallest
applications in hearing aids and small digital watches to the
large heavy-duty lead acid batteries used in the automotive
industry
• The voltage cell was invented by Alessandro Volta (1745-
1827), an Italian physicist in 1792
• A battery or cell is essentially a source of dc electrical
energy. It converts stored chemical energy into electrical
energy through an electrochemical process. This then
provides a source of electric potential difference, or voltage,
to enable currents to flow in electric and electronic circuits.
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Batteries
Primary Batteries – Secondary Batteries – Rechargeable,
Use once, disposable storage or accumulator
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A Battery in Operation
The outer metal case in the form of a
cylindrical container is made of Zinc and
acts as the negative electrode of the cell.
Its base also serves as the negative
terminal of the battery. The cylinder is
filled with a chemical compound which acts
as an electrolyte. In modern batteries this
is in non-liquid form of a paste or dry
compound.
The positive electrode of the cell takes the form of
a Carbon or Graphite rod with a metal cap which is
inserted into the electrolyte in the centre of the
cylinder. The metal cap on the rod serves as the
positive terminal of the battery. 6
A Battery in Operation
When a conducting resistive load is
connected between the positive and negative
terminals of the battery a closed electrical
circuit is formed. Under this condition a
number of chemical reactions take place in
the electrolyte which results in the
generation of positively charged ions and
free negatively charged electrons within it.
The positive ions migrate through the electrolyte towards the carbon rod
and become deposited on it. The electrons, on the other hand, cannot
migrate through the electrolyte because its chemical composition forms a
barrier which inhibits the passage of electrons through. Instead, the
electrons accumulate at the negative electrode of the cell. This gives rise
to an electric potential difference between the two terminals of the battery. 7
A Battery in Operation
The potential difference between the two terminals
of the battery results in an electric field across the
resistive load connected between them. This causes
the electrons to flow in the external electric circuit
through the load and finally to the positive terminal
of the battery.
As long as the closed electric circuit exists, the current continues to flow and the
electrochemical process in the electrolyte continues with the constituent chemicals being
converted into other chemicals. Eventually the supply of original chemicals in the
electrolyte becomes depleted and the voltage generated between the terminals of the
battery drops, ultimately to zero, and the battery becomes discharged.
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A Battery in Operation – Capacity and
Discharge
• There is a limit to the length of time for which a battery
can generate electricity and consequently it has a
limited lifetime or cycle time. The length of time for
which a battery lasts is determined by the amount of
charge it stores in total and the rate at which this
charge is used, which in turn depends on the
magnitude of the current drawn from it.
• A battery will last longer when a low value of current is
drawn from it than it will when a high value of current
is demanded.
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A Battery in Operation – Capacity and
Discharge
• A battery will last longer when a low value of current is drawn
from it than it will when a high value of current is demanded.
This is indicated in figure below, where the terminal voltage of a
battery is plotted against time for different values of current
drawn from it with
I1 < I2 < I3 < I4.
Terminal
Voltage (V)
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A Battery in Operation – Capacity and
Discharge
• One might then expect battery capacity to be
expressed as a quantity of charge in Coulombs.
However, in practice, it proves more useful to express
the battery capacity in terms of the product of current
(in Amperes) and time (in hours). Battery capacity is
therefore expressed in units of Ampere-hours (Ahr).
• It is also important, however, to realise that in practice
there is a maximum current which a battery is able to
deliver and this must also be taken into account when
choosing a suitable battery for a particular application.
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A Battery in Operation – Capacity and
Discharge
Table: Battery Lifetime vs Current Drawn
Battery capacity Battery Capacity Current Drawn Lifetime
expressed in units of 10 Ahr 10 A 1 hr
Ampere-hours (Ahr)
allows the effective 10 Ahr 1A 10 hr
lifetime of the battery to 10 Ahr 20 A 30 mins
be calculated for different 10 Ahr 0.25A 40 hrs
levels of current drawn
1 Ahr 1A 1hr
from it, as indicated in
the following Table. 1 Ahr 5A 12 mins
1 Ahr 100 mA 10 hr
Remember - 1 Ahr battery may not be able to deliver a current as high as 5A due to the limitations of its
chemistry and could not be used in even for a period as short as 12 mins.
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A Battery in Operation – Capacity and
Discharge
Energy storage in AA batteries
Battery Avg. voltage milli-Amp Watt-hours Joules
Type During discharge hours (mAh) Wh J
Alkaline
1.225 1150 1.41 5076
Long-life
Carbon-zinc 1.1 320 0.35 1260
Nickel-Cadmium 1.2 300 0.36 1296
NiMH 1.2 800 0.96 3456
From www.allaboutbatteries.com
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Low-drain discharge of 200mA
designed to represent
a typical light load on a
battery that a toy,
CD/MP3 player, torch
or similar product may
demand from a
battery.
http://www.batteryshowdown.com/index.html
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High-drain discharge of 1000mA
represent a typical
heavy load on a
battery that a digital
camera or similar
power-hungry device
may use.
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A Battery in Operation – Capacity and
Discharge
• A standard 1.5V AA
alkaline battery has an
initial energy store of
1500mAh. Typical
applications use 4 of
these to deliver a peak
voltage ≈ 6V. The
combination may
continue to function
until the delivered
voltage drops to ~4.8V .
This drop in voltage will
occur with time and as a
function of the current
drawn; see discharge
curve below.
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EV Batteries (optional extra)
• Hot topic in battery design
• Comparison of different battery types (pretty technical)
• https://iopscience.iop.org/article/10.1088/1757-
899X/252/1/012058/pdf
• EV Battery Introduction
• https://ocw.tudelft.nl/course-lectures/electric-cars-
technology-12/
• Battery of the Future, EU Brief
• https://ec.europa.eu/environment/integration/research/newsa
lert/pdf/towards_the_battery_of_the_future_FB20_en.pdf
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Electrical Circuits
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What is a circuit?
Talk about nodes!
Figure 1.3 An electrical circuit consists of circuit elements, such as voltage sources, resistances,
inductances, and capacitances, connected in closed paths by conductors.
Aspects we know about..
• Current
• We deal with DC current
• Voltage
• Electric potential
• Resistance
• Resitivity
• Still to come later:
• Capacitance, inductance
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Circuit analysis
Figure 1.6 In analyzing circuits, we frequently start by assigning current variables i1, i2, i3, and so forth.
Kirchhoff’s Current Law
• The net current entering a node is zero
• Might hear it put as:
• The sum of the currents into a node is zero
• The sum of the currents into a node is equal to the sum of the
currents out of the node
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In practice….
Figure 1.18 Partial circuits showing one node each to illustrate Kirchhoff’s current law.
Nodes
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Nodes
Figure 1.19 Elements A, B, C, and D can be considered to be connected to a common node, because all points in a circuit
that are connected directly by conductors are electrically equivalent to a single point
In Series….
Figure 1.20 Elements A, B, and C are connected in series. 26
Kirchhoff’s Voltage Law
• The algebraic sum of the voltages equals zero for any
closed path (loop) in an electrical circuit.
• Loop
• Closed path starting at a node and proceeding though circuit
elements and then returning to that starting node
• Circuits can have many loops
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KCL…
Figure 1.25 Circuit used for illustration of Kirchhoff’s voltage law. 28
KCL…
Figure 1.25 Circuit used for illustration of Kirchhoff’s voltage law. 29
In parallel…
Figure 1.27 In this circuit, elements A and B are in parallel. Elements D, E, and F form another parallel
combination.
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More reading
• How batteries work
• https://www.youtube.com/watch?v=9OVtk6G2TnQ
• Hambley Chapter 1
• Read and go through examples
• We don’t use alternating current in this course or voltages
that change over time
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