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Electrical Engineering
Electrical Circuits
 Electric
charge and current
 What’s
a circuit?
Analogy with water flow
 Resistance
& Ohm’s Law
 Series and parallel circuits
 Kirchhoff’s Laws
 Electric Power
Electrical Circuits
The following quantities are measured in an
electrical circuit*;
Denoted by I and measured in Amperes (A)
Denoted by R and measured in Ohms ( Ω )
Electrical Potential (Voltage):
Denoted by V and measured in volts (V)
* The word circuit has the implication of “circle”
built into it. That’s because the electrons forming
the current have to be conserved and always
need a continuous path.
Electrical Circuits
Current is the movement of electrical charge - the flow of
electrons through the electronic circuit. The direction of a
current flow in a metal wire is from positive to negative (the
opposite direction of electron flow). Current is measured in
Resistance causes an opposition to the flow of electricity in a
circuit. It is used to control the amount of voltage and/or
amperage in a circuit. It is measured in OHMS (Ω).
Voltage is the electrical force that causes current to flow in a
circuit. It is measured in VOLTS .
Electrical Symbols
Electronic components are classed into either
being Passive or Active devices.
Passive Devices contribute no power to a circuit or system. In
fact they may drain electrical power. Examples are resistors,
light bulbs, electrical heaters.
Active Devices are capable of generating voltages or currents.
Examples are batteries and other electrical current and voltage
By using schematics symbols we can represent real-life devices.
Electrical Circuits
Electrical Circuits
Electrical Circuits
Electrical Circuits
Electrical Circuits
Example: Part of a Car’s Electrical Diagram
Ohm’s Law
The ratio of voltage to current is called the resistance,
and if the ratio is constant over a wide range of
voltages, the material is said to be an "ohmic" material.
If the material can be characterized by such a
resistance, then the current can be predicted from the
 V   IR
 V   IR
Kirchhoff’s Voltage Law
 Kirchhoff’s
Voltage Law is a form of the
Conservation of Energy Law.
 KVL states
that the algebraic sum of the
voltages around a closed path in a
circuit is equal to zero.
Σ V(closed loop) = Σ IR(closed loop) = 0
Kirchhoff’s Current Law
 Kirchhoff’s
Current Law is a form of the
Conservation of Charge Law.
 KCL states
that the algebraic sum of the
currents in the branches that converge
to any node is equal to zero
Σ I(node) = 0
Series and Parallel Circuits
Simple circuits are categorized in two types:
Series Circuits
Parallel Circuits
For circuits with series and parallel sections, break the
circuit up into portions of series and parallel, then
calculate values for these portions, and use these
values to calculate the resistance of the entire circuit.
Or, for each individual series path, calculate the total
resistance for that path. Second, using these values, by
assuming that each path as a single resistor, calculate
the total resistance of the circuit.
Resistors in Series
A series circuit is one with all the loads in a
row, like links in a chain. There is only one
path for the electricity to flow.
 Add the resistances together to get the total
Resistors in Parallel
A parallel circuit is one that has two or more
paths for the electricity to flow. In other
words, the loads are parallel to each other.
 Add the inverse of the resistances together to
get the inverse of the total or equivalent
Example: Find the currents in the
following circuit.
Solution: Assign currents to each
part of the circuit between the node
points. We have two node
points that will give us three
different currents. Assume that the
currents move in a clockwise
The current on the segment EFAB
is I1, on the segment BCDE is I3
and on the segment EB is I2.
Solution Continued
 Using
the Kirchhoff's Current Law for the
node B yields the equation
I1 + I2 - I3 = 0
 For the node E we will get the same
equation. Then we use Kirchhoff's
voltage law
- 4×I1+ (-30) - 5×I1 - 10×I1 + 60 +10×I2 = 0
-19I1 + 10I2 = -30
Solution Continued
When we go through the battery from (-) to (+) on
segment EF, potential difference is -30 V, and on
segment FA moving through the resistor of 5W will
result in the potential difference of -5*I1. In a similar
way we can find the potential differences on the other
segment of the loop EFAB.
In the loop BCDE, Kirchhoff's voltage law will yield
the following equation:
- 30×I3 + 120 - 10×I2 + 60 = 0
-10I2 – 30I3 = -180
Solution Continued
Now we have three equations with three unknowns:
1) I1 + I2 - I3 = 0
2) - 19×I1 + 10×I2 = - 30
3) - 10×I2 – 30×I3 = -180
This linear system can be solved by methods of
simple algebra. The system above has the following
I1 = 2.8 A
I2 = 2.4 Amp
I3 = 5.2 Amp
Parallel Circuits
A parallel circuit is a circuit in
which there are at least two
independent paths in the circuit to
get back to the source. In a parallel
circuit, the current will flow through
the closed paths and not through the
open paths.
Consider a simple circuit with an
outlet, a switch, and a 60-watt light
bulb. If the switch is closed, the
light operates. When a second 60watt bulb is added to the circuit in
parallel with the first bulb, it is
connected so that there is a path to
flow through to the first bulb or a
path to flow through to the second
bulb. Note that both bulbs glow at
their intended brightness, since they
each receive the full circuit voltage
of 120 volts.
Parallel Circuits
Every load connected in a separate path receives the full circuit voltage. If a
third 60-watt bulb is added to the circuit, it also glows as intended since it
receives its full 120 volts.
One special concern in parallel circuits is that the amperage from the source
increases each time another load is added to the circuit in parallel. Therefore,
it is very easy to keep adding loads or plugging them in parallel and thereby
overloading a circuit by requiring more current to flow than the circuit can
safely handle.
An obvious advantage of parallel circuits is that the burnout or removal of one
bulb does not affect the other bulbs in parallel circuits. They continue to
operate because there is still a separate, independent closed path from the
source to each of the other loads. That is why parallel circuits are used for
wiring lighting and receptacle outlets. If one light on a parallel circuit burns
out, it is the only one that quits and the other lights wired in parallel stay on.22
Parallel Circuits
The following rules apply to a parallel circuit:
The potential drops of each branch equals
the potential rise of the source. The total
current is equal to the sum of the currents in
the branches.
Parallel Circuits
The inverse of the total resistance of the circuit (also called
effective resistance) is equal to the sum of the inverses of the
individual resistances.
One important thing to notice from this last equation is that the
more branches you add to a parallel circuit (the more things you
plug in) the lower the total resistance becomes. Remember that
as the total resistance decreases, the total current increases.
So, the more things you plug in, the more current has to flow
through the wiring in the wall. That's why plugging too many
things in to one electrical outlet can create a real fire hazard.
DC Circuit Water Analogy
Each quantity in a battery-operated DC circuit has a direct
analog in the water circuit. The nature of the analogies can
help develop an understanding of the quantities in basic
electric circuits. In the water circuit, the pressure P drives
the water around the closed loop of pipe at a certain flow
rate F. If the resistance to flow R is increased, then the flow
rate decreases proportionately.
Current Law and Flow Rate
Current Law and Flow Rate
For any circuit, fluid or electric, that has multiple
branches and parallel elements, the flow rate
through any cross-section must be the same. This
is sometimes called the principle of continuity.
Voltage Law and Pressure
Voltage Law and Pressure
DC Electric Power
The electric power in watts associated with a
complete electric circuit or a circuit component
represents the rate at which energy is converted from
the electrical energy of the moving charges to some
other form, e.g., heat, mechanical energy, or energy
stored in electric fields or magnetic fields.
For a resistor in a D C Circuit the product of voltage
and electric current gives the power:
Power = Voltage x Current
The details of the units are as follows:
DC Electric Power
Convenient expressions for the power dissipated in a
resistor can be obtained by the use of Ohm's Law.
The fact that the power dissipated in a given
resistance depends upon the square of the current
dictates that for high power applications you should
minimize the current. This is the rationale for
transforming power to very high voltages (and low
currents) for cross-country electric power distribution.
Household Electricity
Alternating current or AC electricity is the type of
electricity commonly used in homes and businesses
throughout the world.
The flow of electrons through a wire in direct current (DC)
electricity is continuous in one direction, but the current in AC
electricity alternates back and forth.
The back-and-forth motion occurs between 50 and 60 times per
second, depending on the electrical system of the country.
What is special about AC electricity is that the voltage in can be
readily changed (transformed to higher or lower values), thus
making it more suitable for long-distance transmission than DC
AC Ohm's Law
AC means the driving voltage behaves
sinusoidally and the corresponding
alternating current may lead or lag it.
 The alternating current analog to Ohm's law
where Z is the impedance of the circuit and V
and I are the effective values (root mean
square, or RMS) of the voltage and current.
House Wiring Diagram
Basic AC Circuits
AC circuits have a black
“hot” or power wire, a
white “neutral” or return
wire and a green
“ground” wire.
 The ground wire
protects you from
getting shocked.
Formula Wheel
If you have trouble remembering these
formula, here is a useful tool.
 Electricity
 The
is your friend
governing laws include:
Conservation of electric charge (i.e., electrons)
 Ohm’s Law, V = RI
 Kirchhoff's laws of current an voltage
 Power in a DC dissipative circuit is IV, I R, or