Chapter 2 - Fundamentals of Electric Circuits

Summary

This educational chapter delves into fundamental electrical circuit laws, starting with the concept of resistance, symbolized by the Greek letter rho (ρ), 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 laws—current law (KCL) and voltage law (KVL)—explaining 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

• 🔌 Resistance is a property of materials that impedes the flow of electric current, symbolized by 'R' and measured in ohms (Ω).
• 💧 The concept of resistance is analogous to rocks in water impeding the flow, with resistors in a circuit represented by a zigzag symbol.
• 📐 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.
• 🏗️ Resistance is dependent on the material (ρ), length (L), and cross-sectional area (A) of a conductor, with resistance increasing with length and decreasing with area.
• 🌐 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.
• 🔄 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 voltages around any closed loop in a circuit is zero, reflecting the conservation of energy.
• 🔗 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).
• 🔄 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).
• 🔌 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 (Ω). Resistance depends on the material's resistivity (ρ), the length (L) of the resistor, and the area (A) it covers, as described by the formula R = ρ * (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

00:00

🔌 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 = ρ(L/A), is introduced, where R is resistance, ρ (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.

05:02

⚡ 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.

10:05

🔄 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.

15:06

🔗 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.

20:06

🔄 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.

25:08

🔍 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.

Keywords

💡Resistance

Resistance, denoted by the symbol R, is a fundamental concept in electrical engineering that refers to the opposition to the flow of electric current through a material. In the context of the video, resistance is likened to rocks in water impeding the flow of water, analogous to how resistors impede the flow of electrons in a circuit. The resistance of a material is determined by its intrinsic properties, such as the material type (Greek letter rho, ρ), its length (L), and its cross-sectional area (A). The video explains that resistance is inversely proportional to the area and directly proportional to the length of the material, and it is measured in ohms (Ω).

💡Ohm's Law

Ohm's Law is a cornerstone principle in the study of electrical circuits, which states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with the proportionality constant being the resistance (R) of the conductor. Mathematically, it is expressed as V = I × R. The video uses Ohm's Law to explain how knowing the resistance and current allows one to calculate the voltage across a resistor, and vice versa. It's a fundamental tool for analyzing and designing electrical circuits.

💡Resistors in Series

Resistors are said to be in series when they are connected end-to-end in a single path so that the same current flows through each one. The total resistance in a series circuit is the sum of the individual resistances, as explained in the video with the formula Req = R1 + R2 + R3. This concept is crucial for understanding how the resistance increases with each additional resistor in series, affecting the overall current flow in the circuit.

💡Resistors in Parallel

Parallel resistors are connected in such a way that they share the same voltage across them, but the current is divided among them. The video explains how to calculate the equivalent resistance of parallel resistors using the formula 1/Req = 1/R1 + 1/R2. This is important for understanding how the total resistance decreases as more resistors are added in parallel, which in turn affects the distribution of current in the circuit.

💡Kirchhoff's Laws

Kirchhoff's Laws are two fundamental laws used in circuit analysis: Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). KCL states that the sum of currents entering a node is equal to the sum of currents leaving the node, ensuring charge conservation. KVL states that the algebraic sum of the potential differences (voltages) in any closed loop of a network is zero, reflecting the conservation of energy. The video uses these laws to explain how to analyze complex circuits by breaking them down into simpler components.

💡Conductors

Conductors are materials that allow electricity to flow through them with minimal resistance. The video mentions silver, copper, and aluminum as examples of good conductors due to their low resistance, making them ideal for use in wiring and electrical components. Conductors are the opposite of insulators and are essential for the functioning of electrical circuits.

💡Insulators

Insulators are materials with high resistance that do not conduct electricity well. The video gives examples like glass and Teflon, which are used to prevent the flow of electricity and are crucial in applications where isolation of electrical components is necessary for safety or functionality.

💡Semiconductors

Semiconductors are materials that have electrical conductivity between that of conductors and insulators. They are particularly important in modern electronics because their conductivity can be controlled or modified, making them suitable for a wide range of electronic devices like computers and smartphones. The video touches on how the arrangement of materials in semiconductors can yield unique properties.

💡Voltage Division

Voltage division is a principle used in series circuits where the total voltage across a series of resistors is divided among them in proportion to their resistances. The video explains this concept by showing how to calculate the voltage across a particular resistor in a series circuit using the formula V = (R/Req) × V_total, where R is the resistance of the resistor of interest, and Req is the equivalent resistance of the series circuit.

💡Current Division

Current division is a principle used in parallel circuits where the total current is divided among the parallel paths according to the resistances of each path. The video demonstrates how to calculate the current through a particular resistor in a parallel circuit using the formula I = (R_parallel/R_total) × I_total, where R_parallel is the resistance of the parallel resistor of interest, and R_total is the equivalent resistance of the parallel circuit.

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 = ρ * 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