Kirchhoff's Voltage Law (KVL)

Summary

In this lecture, the speaker explains Kirchhoff's Voltage Law (KVL), stating that the algebraic sum of voltages in a closed loop is zero. Using an example circuit with a voltage source and two resistors, the speaker walks through applying KVL to find the voltage drops across each component. They also introduce two different sign conventions for writing KVL equations, discussing the relationship between voltage, current, and resistance. Lastly, the speaker emphasizes the importance of understanding the concept behind KVL, based on energy conservation, to solve circuits effectively.

Takeaways

• 📏 The lecture begins with a discussion of KVL (Kirchhoff’s Voltage Law), stating that the algebraic sum of all voltages in a closed loop is zero.
• 🔋 In a closed loop with a voltage source (V), a resistor (R1), and another resistor (R2), the sum of voltage drops equals the total voltage supplied.
• 💡 KVL can be applied by adding up the voltage drops across each element in the loop, where voltage drops across resistors are calculated using Ohm’s law (V = IR).
• 🔄 The potential drop across a resistor is determined by multiplying the current (I) by the resistance (R).
• 🔍 Two conventions for writing KVL equations: the first considers a rise in potential as positive, while the second considers a rise as negative.
• 📝 Both conventions lead to the same result, with V = I * (R1 + R2), showing that the total voltage drop equals the source voltage.
• 🌍 KVL is based on the law of conservation of energy, as opposed to KCL (Kirchhoff's Current Law), which is based on the conservation of charge.
• ⚡ Voltage represents potential energy difference, meaning the energy to move a unit charge between two points is independent of the path taken.
• 🎯 KVL equations should include only potential differences (voltages) between points, not individual point potentials.
• 🔁 The lecture emphasizes that regardless of the chosen path in a circuit, following proper rules will always yield consistent results.

Q & A

What is KVL?

KVL stands for Kirchhoff's Voltage Law, which states that the algebraic sum of all the voltages in any closed loop of a network is zero.

How do you apply KVL?

To apply KVL, you calculate the sum of all voltages in a closed loop, considering their signs, and set this sum equal to zero.

What is the significance of the voltage source in the KVL equation?

The voltage source in the KVL equation is represented by 'V' and is considered as a rise in potential, which is typically given a positive sign in the KVL equation.

What is the role of resistors in the KVL equation?

Resistors in the KVL equation represent voltage drops across them, calculated as the product of current (I) and resistance (R), and are typically given a negative sign due to the drop in potential.

How does the direction of current flow affect the KVL equation?

The direction of current flow determines whether the potential rises or drops. A rise in potential is associated with a positive sign, while a drop is associated with a negative sign in the KVL equation.

What are the conventions for writing KVL equations?

There are two main conventions: one where a rise in potential is positive and a drop is negative, and another where the signs are reversed. The choice of convention depends on the direction chosen to traverse the loop.

Why is KVL based on the law of conservation of energy?

KVL is based on the law of conservation of energy because voltage represents the potential energy difference across an element, and the energy required to move a unit charge between two points is independent of the path taken.

How do you calculate the potential difference between two points using KVL?

To calculate the potential difference between two points using KVL, you choose a path between those points, apply KVL up to the second point, and equate the result to the potential at the second point.

Why can't you include the potential at a point directly in the KVL equation?

You can't include the potential at a point directly in the KVL equation because KVL deals with potential differences (voltages), not absolute potentials.

What happens if you apply KVL starting from different points in the circuit?

Applying KVL from different starting points should yield the same result for the potential difference between any two points, as long as the rules are followed correctly.

How does the choice of path affect the KVL equation?

The choice of path affects the order in which voltages are added to the KVL equation, but the final result for the potential difference between any two points should be the same regardless of the path chosen.

Outlines

00:00

🔍 Introduction to KVL and Voltage Calculation in a Closed Loop

In this paragraph, the speaker introduces Kirchhoff's Voltage Law (KVL), which states that the algebraic sum of all voltages in a closed loop is zero. The explanation involves a simple circuit with a voltage source and two resistors. The potential difference between points in the circuit is calculated, illustrating the concept of high and low potential, as well as voltage drops across resistors according to Ohm's law. The paragraph ends by formulating a basic KVL equation.

05:00

⚖️ Understanding Sign Conventions in KVL

This paragraph focuses on two different conventions for writing KVL equations. The first convention assigns a positive sign to rises in potential and a negative sign to potential drops. An example is given where moving through the circuit components leads to forming the KVL equation. The second convention reverses the sign conventions—assigning a negative sign to potential rises and a positive sign to potential drops. Despite the differences in conventions, the final equation remains consistent. The speaker suggests that the second convention is more intuitive for them.

10:03

🔋 KVL and the Conservation of Energy

Here, the relationship between KVL and the law of conservation of energy is explained. KVL is derived from the principle that voltage is a measure of potential energy difference across an element, which remains independent of the path chosen between two points. The speaker provides an example of calculating potential differences between two points, VA and VB, and explains that KVL deals only with voltages or potential differences, not the potentials themselves.

15:06

🧠 Applying KVL to Solve Potential Differences

This paragraph provides a method for solving potential differences using KVL. The speaker explains how to start from a point, apply KVL by considering only potential differences (voltage sources and drops across resistors), and avoid using individual potentials at points in the circuit. An example of solving for VA - VB is presented, showing how to follow different paths in the circuit and still arrive at the same result. The speaker emphasizes the importance of understanding concepts over memorizing formulas.

Keywords

💡KVL (Kirchhoff's Voltage Law)

Kirchhoff's Voltage Law (KVL) states that the algebraic sum of all voltages in a closed loop is zero. This principle is based on the law of conservation of energy and ensures that the total voltage supplied in a circuit equals the total voltage drop across the components. In the script, KVL is applied to a circuit with resistors and a voltage source, where the sum of the voltages is calculated to be zero.

💡Closed loop

A closed loop in an electrical circuit is a complete path through which current flows. The concept of a closed loop is crucial for applying KVL, as the law deals with the total voltage around such loops. In the video, the closed loop consists of a voltage source and two resistors (R1 and R2), through which current I flows.

💡Voltage drop

A voltage drop occurs when electrical energy is lost as current passes through a resistor or other circuit element, following Ohm's Law (V=IR). In the video, the voltage drop across resistors R1 and R2 is discussed, and it is shown that the potential decreases by an amount proportional to the resistance and current (IR).

💡Ohm's Law

Ohm's Law defines the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit, given by the formula V=IR. This principle is used in the video to calculate the voltage drop across resistors, which is critical for applying KVL to find the sum of voltages in the circuit.

💡Potential difference

Potential difference, also known as voltage, refers to the difference in electric potential between two points in a circuit. It drives the current flow in the circuit. The script explains how the potential difference between two points (e.g., A and B) is calculated using KVL, focusing on how the potential changes across resistors and a voltage source.

💡Resistor

A resistor is a component that opposes the flow of current in a circuit, causing a voltage drop as current passes through it. The script uses two resistors, R1 and R2, to demonstrate how voltage drops across them are calculated and incorporated into the KVL equation. The values of the resistances affect the magnitude of the voltage drops.

💡Series circuit

A series circuit is a type of electrical circuit where components are connected end-to-end, so the same current flows through all of them. In the script, the resistors R1 and R2 are connected in series with the voltage source, meaning the current I is the same through both resistors, and KVL can be applied to find the total voltage drop.

💡Conventions for potential rise and drop

These conventions help determine whether a voltage change is positive or negative in a KVL equation. The video explains two conventions: one where a potential rise (from low to high) is positive and a drop (from high to low) is negative, and another where the opposite signs are used. Both conventions lead to the same final KVL equation.

💡Law of conservation of energy

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. KVL is based on this law, as it ensures that the total energy supplied to a closed loop is equal to the energy dissipated across the circuit elements. This principle underpins the video’s explanation of why the sum of voltages in a loop equals zero.

💡KCL (Kirchhoff's Current Law)

Kirchhoff's Current Law (KCL) states that the total current entering a junction in a circuit equals the total current leaving the junction. Although this video focuses on KVL, KCL is mentioned as being based on the conservation of charge, in contrast to KVL’s foundation in the conservation of energy.

Highlights

Introduction to KVL (Kirchhoff's Voltage Law)

KVL states the algebraic sum of all voltages in a closed loop is zero

Explanation of how to calculate the sum of voltages considering their signs

Example of a closed loop with a voltage source and two resistors

Concept of potential difference and how it relates to voltage

How to determine the potential at different points in a circuit

Application of Ohm's law to calculate voltage drop across resistors

Derivation of the KVL equation for the example circuit

Introduction to conventions for writing KVL equations

First convention: rise in potential is positive, drop is negative

Second convention: rise in potential is negative, drop is positive

Explanation of why KVL is based on the law of conservation of energy

How voltage is a measure of potential energy difference

The uniqueness of voltage values and their independence of path

How to apply KVL when calculating potential differences between points

Emphasis on not including point potentials in KVL equations

Demonstration of calculating VA - VB using KVL

Explanation of choosing different paths to calculate potential differences

Final statement on the consistency of results when applying KVL correctly

Encouragement to clarify concepts for easy problem-solving

Transcripts

in the last lecture we had discussion on

KCl and now we are going to understand

what is KVL and how to apply KVL so

let's move on to this statement of KVL

the algebraic sum of all the voltages in

any closed loop is zero so when you

calculate there is a break sum of all

the voltages this means you calculate

the sum of all the voltages considering

their signs then you will find it is

equal to zero in closed loop for example

here we have a closed loop having three

elements first one is the voltage source

providing the voltage V second one is a

resistor having the value R one the

third one is resistor again but having

the value R 2 now let's say the current

in this loop is equal to I and we know

the potential difference or the voltage

is equal to the high potential minus the

low potential let's say this point is

connected to the ground this means here

we will have zero volt as the potential

and therefore here also we will have

zero volt as the potential and therefore

this point is still low potential point

and let's say potential here is equal to

V Prime

this is the high potential point so the

high potential that is V Prime minus the

low potential that is zero volt will be

equal to the potential difference or the

voltage which is V therefore we can say

that V prime is equal to V so the

potential here that is V prime is equal

to V now we know the fact that when

current I passes through resistance r1

there will be four

drop and the voltage drop will be equal

to current I multiplied to r1 following

the Ohm's law here potential is V this

means here also potential will be V and

this potential will get reduced by hi I

1 because this is the potential drop due

to resistance r1 so here we will have

the potential equal to V minus I R 1 hi

r1 so here also we will have the

potential equal to V minus hi hi 1 R 1

and R 2 are connected in series

therefore same current I will flow

through r2 as well and therefore the

drop across R 2 will be equal to I

multiplied to r2 therefore when we move

to this point this potential will reduce

by hi r2 so V minus I R 1 minus hi r2

will be the potential at this point but

this point is having the potential equal

to zero volt this implies V minus I R 1

minus IR to V minus I R 1 minus I R 2 is

equal to zero and this is our KVL

equation so I hope you now understand

how to find the KVL equation but every

time we are not going to analyze this

circuit like this there are some

conventions and following those

conventions you can write down the KVL

equation directly and there are

different ways to write down the KVL

equation here we have followed the

convention in which we are considering

the rise in potential as positive I will

first write down the convention and then

we will follow it in this particular

Rickett so the convention is rise in

potential will give you the positive

sign and the drop in potential who will

give you the negative sign now focus on

this particular voltage source we are

starting from this point and then we

will move back to this point and the

first element we are encountering is a

voltage source now when you move from

this point to the upward direction you

can see that we first encountered the

negative terminal this means the low

potential point and then we encountered

the positive terminal

this means the high potential point so

low to high

this means rising potential and

therefore we will have the positive sign

for V so we will write plus V then we

will keep on moving and we encountered a

resistance r1 so here we are having the

voltage drop by I R 1 and we know

resistor will dissipate the power and

therefore current will enter the

positive terminal and it will leave the

negative terminal we have already

discussed at this point in great detail

so here you can see that we first

encountered the high potential point and

then we encountered the low potential

point so there is drop in potential

hence we will have the negative sign so

negative I r1

I R 1 similarly here also we will have

the drop in potential therefore we will

write minus hi r2 and this will be equal

to 0

so you can see that we have the same

equation and from here we can say that V

is equal to AI

r1 plus r2 now I will give you the

second convention and according to this

convention the rise in potential will

give you the negative sign opposite of

this convention and the drop in

potential who will give you the positive

sign this convention is reversed here

and now we will obtain the KVL equation

following the new convention we will

start from this point and we will

encounter an element that is the voltage

source and you can see that we are

having the rise in potential therefore

we will have the negative sign so minus

V then we encounter another element that

is a resistor and here we are having the

fall or drop in potential therefore we

will have the positive sign and then we

have I R 1 i R 1 similarly we have plus

I R 2 for resistor r2 plus hi r2 and the

sum we are going to get is equal to 0

and from this equation we can say that

voltage V is equal to I multiplied to r1

plus r2 the same result now please let

me know in the comment section which

convention do you want to follow I

personally like to follow this

convention because this makes more sense

to me now

we will move on to the last point and

according to this point

KVL his based on law of conservation of

energy

KCl was based on law of conservation of

charge but KVL is based on law of

conservation of energy the voltage is

the measure of potential energy

difference across the element we know

this point

and we also know that there is a single

unique value of a voltage therefore the

energy required to move a unit charge

from one point to other his independent

of the path chosen you will get the same

voltage or potential difference between

the two points irrespective of the path

you have chosen for example let's say

this point his point a and this point

his point B and potential here is equal

to VA and potential here is equal to VB

and we want to calculate the potential

difference VA minus VB that is we want

to calculate the difference in the

potentials of the point a and the point

B we want to have the potential

difference VA minus VB and due to our

initial analysis we know the potential

at Point a is equal to zero volt and the

potential at point B is equal to V minus

I R 1 so we can write VA minus VB equal

to 0 minus V minus I R 1 or we can write

minus V plus I R 1 so this is the

potential difference VA minus VB the

potential difference between the point a

and the point B but every time you won't

have the potentials at the two points

and therefore you must know how to apply

KVL when you are required to calculate

the potential difference between the two

random points in the circuit and we know

KVL is the voltage law voltage means the

potential difference and therefore in

the KVL equation you will only have the

voltage or potential difference all the

three values here our voltages V is the

voltage hi r1 is

I r2 is also a voltage so you cannot

include the potential at a point in KVL

equation this means you cannot include

VA and you cannot include VB but you can

include VA minus VB because VA minus VB

is the potential difference or the

voltage so I will now explain how to

deal with this kind of problem whenever

you have to deal with the potentials at

a point then pick one point for example

pique then write down the potential at

ay that is VA I will write here then

simply apply KVL up to this particular

point move in this direction you will

have a voltage source V following this

convention we will write plus V Plus V

then we will move forward and have one

resistance therefore we will have minus

hi hi 1 now when you move at this point

then don't write VB like this and equate

it with zero you have to write equal to

and then instead of equating with zero

equate it with V B now in this scenario

when you subtract V B from both the

sides you have VA minus VB plus V minus

y1 equal to zero now this is proper KVL

equation this is one very powerful way

and we will use it a lot to solve the

questions in this course so from here we

will have VA minus VB equal to minus V

Plus hi hi 1 the same result there is

one point I want to clear you can see

that while applying the KVL starting

from the point a we did not included the

potential here which

we so whenever you apply kvl from one

point to another point don't include the

other potentials at point because your

KVL will then be in valid so simply

start with potential at a point and then

include only potential differences and

then finally equate everything with the

final points potential so I hope this

was clear now we have chosen one path to

calculate VA minus VB we can choose

another path as well

so now let's calculate VA minus VB

following this path we will start from

point A and we will have VA then we will

have plus I R 2 plus i r2 and then we

will stop at point B therefore we will

equate with potential VB from here we

are getting VA minus V B equal to minus

hi r2 and VA minus VB we have calculated

should be equal therefore minus V plus I

R 1 should be equal to minus I R 2 this

implies we will have minus V plus I R 1

equal to minus I R 2 and from here we

can say that V is equal to Y R 1 plus R

2 the same result so whatever you do in

the circuit following the proper rules

you will finally have the same result

you don't have to mug up anything you

simply have to clear your concepts and

if your concepts are clear you can

easily solve any network so I hope this

lecture was clear to you and if you have

any doubt you may ask in the comment

section I will hand this lecture here

see you in the next one

[Applause]

you

[Music]