Download Electric Circuits - Gate, IES, TANCET, Engineering

ELECTRIC CIRCUITS BASICS
Electricity Basics
Electricity starts with electrons. Every atom contains
one or more electrons. Electrons have a negative
charge.
Simplest model
of an atom
Atoms will have the same number of
Electrons in the orbit as there are Protons
in the center.
Electrons (29 total)
Valence Ring
(Outer Ring)
Protons (29 total)
A Copper Atom
But most metals have electrons that can detach from
their atoms and move around. These are called free
electrons. Gold, silver, copper, aluminum, iron, etc.,
all have free electrons. The loose electrons make it
easy for electricity to flow through these materials, so
they are known as electrical conductors. They
conduct electricity. The moving electrons transmit
electrical energy from one point to another.
Electrical Circuits
Whether you are using a battery, a fuel cell or a solar
cell to produce electricity, there are three things that
are always the same:
The source of electricity will have
two terminals: a positive terminal
and a negative terminal.
•The source of electricity (whether it is a generator,
battery, etc.) will want to push electrons out of its
negative terminal at a certain voltage. For example, a
AA battery typically wants to push electrons out at 1.5
volts.
•The electrons will need to flow from the negative
terminal to the positive terminal through a copper wire
or some other conductor. When there is a path that
goes from the negative to the positive terminal, you
have a circuit, and electrons can flow through the
wire.
Basic Electrical Circuits
Conductor
(Wire)
Battery
Resistor
(Voltage Source)
(Light Bulb)
Conductor
How does electricity flow?
What causes electrons to move from atom to atom?
Voltage
-
-
-
-
-
-
-
++
+
++
+
++
+
++
+
-
-
-
-
(Pressure)
(Electromotive Force)
Voltage Voltage
Pushes Voltage
the
Pushes
electrons
Voltage
Pushes
the electrons
Voltage
Pushes
the electrons
Pushes
the electrons
the electrons
How does electricity flow?
What causes electrons to move from atom to atom?
-
Voltage
-
-
-
-
-
++
+
++
+
-
-
- - - - ++
+
- - ++
+
(Pressure)
(Electromotive Force)
-
Voltage Pushes the electrons
-
How does electricity flow?
What causes electrons to move from atom to atom?
-
-
-
-
-
-
++
+
++
+
-
-
- - - - ++
+
-
- - ++
+
-
Voltage Pushes the electrons
How does electricity flow?
What causes electrons to move from atom to atom?
Voltage
-
-
-
-
-
++
+
++
+
-
-
- - - - ++
+
- - ++
+
(Pressure)
(Electromotive Force)
-
-
The flow of the electrons is referred to as Current
How does electricity flow?
What causes electrons to move from atom to atom?
-
-
-
-
-
-
++
+
++
+
-
-
- - - - ++
+
-
- - ++
+
-
Electron Flow is measured in Amps
The flow of the electrons is referred to as Current
Electric Circuits
Now that we have the concept of voltage, we
can use this concept to understand electric
circuits.
Just like we can use pipes to carry water, we
can use wires to carry electricity. The
flow of water through pipes is caused by
pressure differences, and the flow is
measured by volume of water per time.
Electric Circuits
In electricity, the concept of voltage will be
like pressure. Water flows from high
pressure to low pressure; electricity flows
from high voltage(higher potential) to
low voltage(lower potential).
But what flows in electricity? Charges!
How do we measure this flow? By Current:
current = I = Dq / Dt
UNITS: Amp(ere) = Coulomb / second
Electrical Network
• A combination of various electric
elements (Resistor, Inductor, Capacitor,
Voltage source, Current source)
connected in any manner what so ever is
called an electrical network. We may
classify circuit elements in two categories,
passive and active elements.
Active Elements
• The elements that supply energy to the
circuit is called active element. Examples
of active elements include voltage and
current sources, generators, and
electronic devices that require power
supplies.
Passive Elements
• The element which receives energy (or
absorbs energy) and then either converts
it into heat (R) or stored it in an electric
(C) or magnetic (L ) field is called passive
element.
Circuit Symbols
18
Voltage Sources:
batteries and power supplies
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?
Voltage Sources:
batteries and power supplies
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).
Circuit Elements
In this first part of the course we will consider two
of the common circuit elements:
resistor
capacitor
inductor
The resistor is an element that “resists” the flow
of electricity.
The capacitor is an element that stores charge for
use later (like a water tower).
Inductor stores charge in the form of magnetic
field
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.
Resistance
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.
Resistance
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.
As was the case in fluid flow, the amount of
resistance depends on the materials and
shapes of the wires.
Resistance
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:
PE = q*V .
Power is the change in energy with respect to
time:
Power = DPE / Dt .
Putting these two concepts together we have:
Power = D(qV) / Dt = V(Dq) / Dt = I*V.
Electrical Power
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.
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?
Example
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.
Example
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 .
Two basic ways
There are two basic ways of connecting two
resistors: series and parallel.
In series, we connect resistors together like
railroad cars:
+
-
+
high V
-
low
R1
R2
Series
If we include a battery as the voltage source,
the series circuit would look like this:
R1
+
Vbat
R2
Note that there is only one way around the
circuit, and you have to go through BOTH
resistors 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
going through either one resistor or the
other: you have a choice!
High V
R1
R2
Low V
Parallel Circuit
If we include a battery, the parallel circuit
would look like this:
+
Vbat
+
R1
-
+
R2
-
Formula for Series:
To see how resistors combine to give an
effective resistance when in series, we can
look either at
R1
I
V = I*R,
+
V1 V
R2
or at
Vbat
2
R = rL/A .
Formula for 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.
Formula for 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 V = IR)
where the V’s add and are in the numerator!
Formula for Parallel Resistors
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
+
Vbat
I1
-
R1 I2
R2
Formula for Parallel Resistors
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.
Formula for Parallel Resistors
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 .
Review:
Resistors: V = IR
Power = IV; R = rL/A
Series: Reff = R1 + R2
Parallel: 1/Reff = 1/R1 + 1/R2
series gives largest Reff, parallel gives smallest Reff.
Class Problem
What is the equivalent
resistance of this network
of resistors?
42
Capacitance
A water tower holds water. A capacitor
holds charge.
The pressure at the base of the water tower
depends on the height (and hence the
amount) of the water. The voltage across a
capacitor depends on the amount of charge
held by the capacitor.
Capacitance
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.
Energy Storage
Note that previously we had:
PE = q*V ,
and now for a capacitor we have:
E = (1/2)*Q*V .
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
Parallel Circuit
If we include a battery, the parallel circuit
would look like this:
+
Vbat
+
C1
+
C2
Review of Formulas
For capacitors in SERIES we have:
1/Ceff = 1/C1 + 1/C2 .
For capacitors in PARALLEL we have:
Ceff = C1 + C2 .
Note that adding in series gives Ceff being
smaller than the smallest, while adding in
parallel gives Ceff being larger than the
largest!
Review:
Capacitors: C = Q/V
PE = ½CV2;
Series: 1/Ceff = 1/C1 + 1/C2
Parallel: Ceff = C1 + C2
series gives smallest Ceff, parallel gives largest
Resistors: V = IR
Power = IV; R = rL/A
Series: Reff = R1 + R2
Parallel: 1/Reff = 1/R1 + 1/R2
series gives largest Reff, parallel gives smallest
Kirchhoff’s Rules
• KVL
“The sum of potential changes around any closed
loop is zero”
rise in potential = drop in potential
• KCL
“algebraic sum of all currents entering a node
is zero”
Current into a junction = current out of a junction
52
• KCL states that at any node (junction) in a
circuit the algebraic sum of currents
entering and leaving a node at any instant of
time must be equal to zero. Here currents
entering(+ve sign) and currents leaving (-ve
sign) the node must be assigned opposite
algebraic signs.
• KVL states that in a closed circuit, the
algebraic sum of all source voltages must be
equal to the algebraic sum of all the voltage
drops.