Chapter 2 - Fundamentals of Electric Circuits
Summary
TLDRThis educational chapter delves into fundamental electrical circuit laws, starting with the concept of resistance, symbolized by the Greek letter rho (Ο), which is influenced by material properties, length (L), and area (A). It introduces Ohm's law, V=I*R, linking voltage, current, and resistance. The chapter continues with Kirchhoff's lawsβcurrent law (KCL) and voltage law (KVL)βexplaining how they govern charge flow and voltage drops in circuits. It further explores resistor configurations in series and parallel, detailing how to calculate total resistance and voltage/current distribution, which are crucial for understanding circuit behavior.
Takeaways
- π Resistance is a property of materials that impedes the flow of electric current, symbolized by 'R' and measured in ohms (Ξ©).
- π§ The concept of resistance is analogous to rocks in water impeding the flow, with resistors in a circuit represented by a zigzag symbol.
- π Ohm's Law (V = I * R) is fundamental, relating voltage (V), current (I), and resistance (R), and indicating that higher resistance results in higher voltage for a given current.
- ποΈ Resistance is dependent on the material (Ο), length (L), and cross-sectional area (A) of a conductor, with resistance increasing with length and decreasing with area.
- π Conductors like silver, copper, and aluminum have low resistance and are used in electrical wiring, while insulators like glass and Teflon have high resistance and prevent current flow.
- π Kirchhoff's Current Law (KCL) states that the sum of currents entering a node must equal the sum of currents leaving the node, preventing charge accumulation.
- π Kirchhoff's Voltage Law (KVL) asserts that the algebraic sum of voltages around any closed loop in a circuit is zero, reflecting the conservation of energy.
- π In a series circuit, resistors are connected end-to-end, sharing the same current, and the total resistance is the sum of individual resistances (R_total = R1 + R2 + ... + Rn).
- π In a parallel circuit, resistors are connected side-by-side, sharing the same voltage, and the total resistance is found by the reciprocal formula (1/R_total = 1/R1 + 1/R2 + ... + 1/Rn).
- π Voltage division occurs in series circuits, where the voltage across each resistor is proportional to its resistance, while current division occurs in parallel circuits, distributing current based on resistance values.
Q & A
What is the basic concept of resistance in electrical circuits?
-Resistance is the opposition to the flow of electric current. It is measured in ohms and symbolized by the Greek letter Omega (Ξ©). Resistance depends on the material's resistivity (Ο), the length (L) of the resistor, and the area (A) it covers, as described by the formula R = Ο * (L/A).
What is Ohm's law and how is it represented mathematically?
-Ohm's law states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through it, with the resistance (R) being the constant of proportionality. Mathematically, it is represented as V = I * R.
What is the significance of different materials having different resistances?
-Different materials have varying resistances which categorize them as conductors, semiconductors, or insulators. Conductors like silver and copper have low resistance and allow electricity to flow easily, while insulators like glass and Teflon have high resistance and prevent the flow of electricity.
What does Kirchhoff's Current Law (KCL) state?
-Kirchhoff's Current Law states that the total current flowing into a junction (node) is equal to the total current flowing out of that junction. In other words, the algebraic sum of currents at a node is zero, expressed as the sum of incoming currents minus the outgoing current equals zero.
How is Kirchhoff's Voltage Law (KVL) different from Kirchhoff's Current Law?
-Kirchhoff's Voltage Law states that the sum of the voltages around any closed loop in a network is zero. This means that the total voltage gain around a loop is equal to the total voltage loss, which is different from Kirchhoff's Current Law, which deals with the conservation of charge at a node.
What is the total resistance when resistors are connected in series?
-When resistors are connected in series, the total resistance (Req) is the sum of all individual resistances. So, if you have resistors R1, R2, and R3 in series, Req = R1 + R2 + R3.
How do you calculate the voltage across a single resistor in a series circuit?
-In a series circuit, the voltage across a single resistor (V3) can be calculated using the formula V3 = (R3 / Req) * V, where R3 is the resistance of the resistor in question, Req is the total resistance of the series circuit, and V is the total voltage supplied.
What is the formula for calculating the equivalent resistance of parallel resistors?
-For resistors in parallel, the equivalent resistance (Req) is calculated using the formula 1/Req = 1/R1 + 1/R2 + ..., which can be rearranged to Req = (R1 * R2) / (R1 + R2) for two resistors.
How does current division work in a parallel circuit?
-In a parallel circuit, current division occurs such that the total current (I) supplied to the parallel combination is divided among the parallel resistors. The current through each resistor (i1, i2) can be calculated using the formula i1 = (R2 / (R1 + R2)) * I and i2 = (R1 / (R1 + R2)) * I.
What is the difference between an open circuit and a closed circuit in terms of resistance?
-An open circuit has infinite resistance, meaning no current flows as the circuit is incomplete. A closed circuit has very low resistance, allowing current to flow freely as the circuit is complete.
Outlines
π Introduction to Electrical Circuit Laws
This paragraph introduces the fundamental concepts of electrical circuits, starting with the concept of resistance. Resistance is likened to an obstruction in a water flow, with rocks in water acting as resistors. The formula for resistance, R = Ο(L/A), is introduced, where R is resistance, Ο (rho) is the material property, L is the length, and A is the area. The paragraph explains how resistance affects the flow of current, with higher resistance impeding flow and lower resistance allowing it to pass more freely. Ohm's law is briefly mentioned as a foundational principle in understanding electrical circuits.
β‘ Ohm's Law and Material Resistance
The paragraph delves into Ohm's law, which is expressed as V = I * R, where V is voltage, I is current, and R is resistance. It explains that the voltage across a resistor can be calculated if the resistance and current are known. The concept of an open circuit, where resistance is infinite, and a closed circuit, where resistance is minimal, is introduced. The paragraph also discusses the resistance of different materials, categorizing them as conductors with low resistance (like silver, copper, and aluminum), insulators with high resistance (like glass and Teflon), and semiconductors with resistance values in between.
π Kirchhoff's Laws in Circuit Analysis
This section introduces Kirchhoff's laws, which are essential for analyzing electrical circuits. Kirchhoff's current law (KCL) states that the sum of currents entering a node must equal the sum of currents leaving the node, preventing charge accumulation. Kirchhoff's voltage law (KVL) asserts that the algebraic sum of the voltages around any closed loop in a circuit is zero. These laws are fundamental for understanding and calculating the behavior of complex circuits.
π Series and Parallel Circuits
The paragraph explains the concepts of series and parallel circuits. In a series circuit, the same current flows through all components, and the total resistance is the sum of individual resistances (R_total = R1 + R2 + R3). The voltage across a specific resistor in a series circuit can be found using voltage division. In contrast, in a parallel circuit, components share the same voltage across them, and the total resistance is calculated by taking the reciprocal of the sum of the reciprocals of individual resistances (1/R_total = 1/R1 + 1/R2). The paragraph also discusses the concept of current division in parallel circuits, where the total current is distributed among the parallel paths.
π Further Exploration of Parallel Circuits
This paragraph continues the discussion on parallel circuits, focusing on current division. It explains how to calculate the current through individual resistors in a parallel circuit using the formula I = (R_parallel / (R1 + R2)) * V, where R_parallel is the equivalent resistance of the parallel combination. The paragraph emphasizes the importance of understanding current division for analyzing and designing electrical circuits with multiple parallel paths.
π Summary of Series and Parallel Concepts
The final paragraph summarizes the key points about series and parallel circuits. It reiterates the principles of voltage division in series circuits and current division in parallel circuits. The paragraph concludes with a brief mention of the practical applications of these concepts in devices like computers and cell phones, highlighting the importance of understanding series and parallel configurations in electrical engineering.
Mindmap
Keywords
π‘Resistance
π‘Ohm's Law
π‘Resistors in Series
π‘Resistors in Parallel
π‘Kirchhoff's Laws
π‘Conductors
π‘Insulators
π‘Semiconductors
π‘Voltage Division
π‘Current Division
Highlights
Introduction to electrical circuit laws starting with resistance.
Explanation of Ohm's law: V = I * R.
Discussion on resistors in series and their impact on current.
Introduction to Kirchhoff's laws: voltage law and current law.
Illustration of how resistance is calculated (R = Ο * L / A).
Comparison of different materials' resistance levels.
Definition of conductors and insulators based on resistance.
Explanation of semiconductors and their properties.
Kirchhoff's current law (KCL) and its application in circuit analysis.
Kirchhoff's voltage law (KVL) and its significance in circuit loops.
Total resistance calculation for resistors in series.
Voltage division principle in series circuits.
Introduction to resistors in parallel and their characteristics.
Calculation of equivalent resistance for resistors in parallel.
Current division principle in parallel circuits.
Practical applications of resistance, series, and parallel concepts in everyday electronics.
Transcripts
hi
in this chapter we'll cover the basic
electrical circuit laws
we will start out by talking about
resistance
and move to
Ohm's law
from Ohm's law we'll talk about
resistors in series in parallel
additionally we will cover kirchhoff's
laws
kirchhoff's laws include kirchhoff's
voltage law
and kirchhoff's current law
so let's get started on this chapter
we will start by discussing resistance
re
resistance
resistance
comes from the base word resist
meaning to stop
right resist meaning to stop so
resistance so if we talk about our
example where we have water
remember this example with water and
then we have current flowing right this
is the current
if we want to discuss resistance
we would have
rocks in the water so these are rocks
and these would be our
resistors
the resistors block the flow they stop
the flow
so these are resistors
here
now discussing our resistance here
if you think of this as a resistor and
we draw resistors in this manner this is
how we would draw them in a circuit
but a resistor is made up of a certain
amount of material it's made of a
material
and so the resistance
resistance r
is equal to
this material property
the Greek letter rho this is a Greek
letter rho
times l
L here
over
a
so big resistances stop a lot of flow of
current
small resistance let current go by
quickly
so if we talk about resistance
it depends on the material
the material
and the length
how long this is and the area
so a big area if a is very big
then the resistance goes down
resistance is
if a
is big
and likewise if
L is big if L is big
the resistance goes up
if
L is big
so it goes down if a is big and the
resistance goes up if L is big
resistance is measured in ohms
so resistance
resistance
is in
ohms
ohms and we write ohms
as this symbol Omega
so this is omega
we write the ohms as Omega because they
both have o
ohms
Omega
so if we talk about a battery
so this is a battery
and we have positive negative and we
connect wires to here
and there's a gap in between here
R is equal to Infinity
all right this is what we call an open
circuit an open circuit where the
resistance is infinity
okay
now if we
connect those wires
we connect those wires
the current flows
and I becomes very big
so our resistance here is approximately
zero very close to zero if we connected
battery this way
okay so we have resistance being very
big and resistance being very small is
zero
now let's take a look at Ohm's law
so Ohm's law
this is very important in this class
Ohm's law
we have
V
equals I
times r
so what does this mean
if we have a resistor that has a
resistance of r
and we know the current I how fast it's
flowing
the current I
we can then figure out the voltage
across this resistor and this is from
plus to minus positive negative so V
equals I times r b equals I times r
so
if
R is very big
if R becomes very big with I
the voltage is very big
and if R becomes very small
the voltage becomes small
so this relationship here is called
Ohm's law
okay so now let's take a look at
different resistances of different
materials of different materials
so on the left here
we have different materials
and then we have their resistance
so
we have silver
which is very expensive cost a lot of
money
and it has a very low resistance meaning
that
electricity or electrons are going to
flow very quickly through it
so we use silver in computers
parts to make sure that things are
conductive so we call things with very
small resistances conductors
copper we find that in most of wires or
electricity wires are made of copper
aluminum is also a good conductor here
and gold more expensive than silver all
of these are good conductors because
they have very low resistance very small
okay and then
on the other side
we have things with very high
resistances very big
okay so glass
Teflon is a plastic
so teflon's a plastic and these have
very high resistances
so they are very good at insulating
insulating or now not allowing
electricity to flow so they stop
electricity
and then in the middle here we have
things that are
in the middle they they are not big they
are not small just in the middle and we
use these
materials
for semiconductors
so depending on how we arrange these
materials we can get some very
interesting properties out of these
materials which is a good thing when
we're talking about computers cell
phones all of those things are used use
semiconductors
let's start by talking about kirchhoff's
current law kirchhoff's current law
sometimes called KCl
so kirchhoff's current law
k c l
okay so let's say we have a node here
this is a node
and we have currents
we have i1
we have I2
and we have
i3
so this states that a charge cannot
build up at a node so what goes in must
come out
okay so we have something called we set
the N equal to the out
for the current
so we're looking at current so coming in
we have I2
Plus
I'm sorry i1
plus I2
equals
equals the out so both of these are
coming in
this one is going out so we have i3
now we can rearrange this equation
or i1 plus I2
minus I3 equals zero so these are the
same thing whatever one you want to use
you can use so these are the same thing
and that is kirchhoff's current law
now let's move to kirchhoff's voltage
law so kirchhoff's voltage law
and kirchhoff's current law is KCl
kirchhoff's voltage law is k v l k v l
kirchhoff's voltage law
and this one
let me draw this
so these are resistors this is a
resistor this is a resistor
and we'll call this V2 B3 these are the
voltages across each resistor we'll call
this V1
and this is V5 and this will be V4 one
two three four five
and
what we're looking at here is the
voltage around a loop
okay so if we start here
and we go around
all the way around this Loop we call
this a loop
so that's a loop
a loop
and what we know is the voltage around
the outside of this is equal to zero
okay
so let's start right here we're starting
here
and if we go negative to positive this
direction we say that's positive so we
have V1 so this is positive
now we go negative or positive to
negative positive to negative and that
is then a negative value so we have
minus V2
and then we have another one positive to
negative that's V3 so we have negative
V3
and then we go to V4 here and that's
negative to positive negative to
positive so that's a positive now and
that's V4
and then we have V5 which is positive to
negative
and we set that equal to zero okay so
the voltage is around a loop must equal
zero must equal zero and
the signs that we use are
this sign this sign this sign this sign
and this sign so it's positive negative
negative positive negative right so we
have this here
and this is kirchhoff's voltage law so
two laws kirchhoff's current law and
kirchhoff's voltage law
let's talk about resistors in series and
resistors in parallel those series and
parallel
let's take a look at this
so
if we have
the same
current
we say that they are in series
for example
we have a voltage source
and we have three resistors
one two three
so this is V
and we have R1
R2
and R3
and
R1 R2 and R3
we say that R1 is in series with R2
and R2 is in series with R1
but R1 is also in series with R3 and R2
is also in series with R3 so R1 R2 and
R3 are all in series series
are all in series
because
the current
i1
I2
and i3
i1 equals I2 which equals
which equals i3
so they have the same current or the
equal
current
i1 equals I2 which equals i3
so we say that they're in series
now we can do several things with this
let's say
let's erase this quick
we have
we want to figure out the total
resistance so the total resistance
we can simplify this circuit
we have voltage here
and this is the equivalent resistance
req meaning equal
this is V
so we want the equivalent resistance
so req
is equal to R1 plus R2 plus R3 R1 plus
R2
plus r 3.
this is the equivalent resistance so
adding all of these together R1 plus R2
plus R3
now
what if we want the voltage across
resistance three we want this voltage
V3
what does that equal to
well to figure that out we have an
equation
R3
equals R1 plus R2 plus R3
times
V times this
and so if we want to figure out the
voltage across R3 we use that resistance
divided by the total resistance the
equivalent resistance R1 plus R2 plus R3
times V this value
and this is what we called
voltage
division
so dividing it so taking apart so taking
a full thing and dividing it dividing it
so voltage division
this is voltage division
now let's talk about parallel
so here we said equal current through
resistors means series
now we're going to talk about parallel
so parallel
means same
voltage or equal voltage
so this is parallel
and we say parallel can be written as
two lines like this meaning parallel
lines parallel lines so parallel lines
meaning parallel
so if we draw a circuit
and we have a current source for current
here
and we have R1 and R2
these are these two resistors are in
parallel because they have the same
voltage across them
so if we talk about the voltage V1
V2
V1 equals V2 same voltage meaning that
they're in parallel
okay
so what if we want to add these
resistors together
so if we add them together just to get
one resistor
we want R equivalent
so if we add these together how do we do
that
well
1 over r e q
equals 1 over R1 plus 1 over R2
so this is one divided by R1 sometimes
in English we say 1 over R1
1 over R1 over
1 over R1 1 over R2 or 1 divided by R1
plus 1 divided by R2 and this is the
equivalent resistance here
so this can be sometimes a little
difficult because you need to add them
up and then take the reciprocal of them
so we can rewrite this equation
our EQ equals R1 times R2 divided by R1
plus R2
these are the same
these are the same same equation
so you can use this one or you can use
this one it's up to you I like this one
better because if you have more
resistors if you have more resistors
here you can just add
more on to here so if you have more
resistors over here somewhere you can
add on to this
okay
so that is the equivalent resistance
now when things were in series we had
voltage division
in parallel now we have parallel we have
current division
so if we look at
i1
and I2
i1 goes through here I2 here
so i1
is equal to
R2 over R1 plus R2
times I this I
so if we want the current i1 we use this
resistor divided by this
plus this R2 divided by R1 plus R2 so we
need to use the opposite resistor
and likewise I2 would be R1 divided by
R1 plus R2 times I
okay and this is what we call
current
division
so we're dividing the current so we're
taking one piece and we're dividing it
so current division
current division
so now that is series and parallel
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