thevenin's theorem explanation | Thevenin's Theorem Solved Example Problem

Summary

This video explains how to calculate the current through an 8-ohm resistor using Thevenin's Theorem. The process involves finding the Thevenin equivalent resistance (Rth) and Thevenin equivalent voltage (Vth) by first turning off independent sources and applying Kirchhoff's Voltage Law (KVL). After calculating Rth and Vth, these values are substituted into Thevenin's equivalent circuit to find the load current through the 8-ohm resistor, which is 1.446 amps. For more details, viewers are directed to install the app and access free electrical circuit notes.

Takeaways

• 📘 The video explains how to find the current through an 8-ohm resistor using Thevenin's theorem.
• 🔌 Thevenin's theorem states that a linear two-terminal circuit can be replaced by a voltage source (Vth) in series with a resistor (Rth).
• 🛠️ Vth is the open circuit voltage at the terminals, and Rth is the equivalent resistance when independent sources are turned off.
• 📊 The current through the load resistor RL can be calculated using I = Vth / (Rth + RL).
• 🔄 To find Rth, turn off all independent sources and calculate the equivalent resistance of the remaining circuit.
• 🔍 The calculation involves finding the parallel resistance of 6 ohms and 10 ohms, which gives an Rth of 3.75 ohms.
• 📏 To find Vth, apply Kirchhoff’s Voltage Law (KVL) to the outer loop of the circuit.
• ⚡ The current in the circuit is found to be 0.5 amperes using KVL.
• 🖋️ The value of Vth is calculated as 17 volts using KVL in the inner loop.
• 📐 After finding both Vth and Rth, the current through the 8-ohm load resistor is calculated as 1.446 amperes.

Q & A

What is Thevenin's theorem?

Thevenin's theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source (Vth) in series with a resistor (Rth). Vth is the open circuit voltage at the terminals, and Rth is the equivalent resistance at the terminals when all independent sources are turned off.

What is the purpose of using Thevenin's theorem in the circuit?

Thevenin's theorem simplifies complex circuits by allowing the calculation of the current through a specific resistor (load resistor) by reducing the circuit to a simple equivalent circuit with a voltage source and a series resistor.

How do you find the Thevenin resistance (Rth)?

To find Rth, you turn off all independent sources in the circuit, which means short-circuiting voltage sources and removing the load resistor (RL). Then, calculate the equivalent resistance of the circuit seen from the open terminals where RL was connected.

How is the equivalent resistance Rth calculated in this particular circuit?

In the circuit provided, the 6-ohm and 10-ohm resistors are in parallel. The equivalent resistance is calculated as 6 * 10 / (6 + 10), which gives 3.75 ohms.

How do you find the Thevenin voltage (Vth)?

To find Vth, remove the load resistor (RL), and calculate the open circuit voltage across the terminals where RL was connected. This is done using Kirchhoff's Voltage Law (KVL) to calculate the current and voltage in the circuit.

What is the formula for calculating the current through the load resistor using Thevenin’s theorem?

The current through the load resistor (I) is given by the formula: I = Vth / (Rth + RL), where Vth is the Thevenin voltage, Rth is the Thevenin resistance, and RL is the load resistor.

What value is calculated for the current through the 8-ohm resistor in this circuit?

The current through the 8-ohm resistor is calculated to be approximately 1.446 A using the formula I = Vth / (Rth + RL).

How is Kirchhoff’s Voltage Law (KVL) used in this circuit analysis?

KVL is applied to the outer loop to calculate the total voltage and current in the circuit. It states that the algebraic sum of all voltages around a closed loop is zero. This principle is used to find the current and voltage across components.

What values are substituted in the formula to calculate the current through the load resistor?

In the formula I = Vth / (Rth + RL), the values substituted are: Vth = 17 V, Rth = 3.75 ohms, and RL = 8 ohms, which gives the current I = 1.446 A.

What steps are involved in finding the Thevenin equivalent circuit?

The steps are: 1) Find the Thevenin resistance (Rth) by turning off all independent sources and calculating the equivalent resistance. 2) Find the Thevenin voltage (Vth) by removing the load resistor and calculating the open circuit voltage. 3) Replace the original circuit with the Thevenin equivalent circuit, consisting of Vth in series with Rth, and the load resistor RL. 4) Calculate the current through the load resistor.

Outlines

00:00

🔧 Understanding Thevenin’s Theorem in Circuit Analysis

The paragraph introduces a tutorial on solving a circuit problem using Thevenin’s theorem. The process aims to find the current through an 8-ohm resistor. Thevenin’s theorem states that any linear two-terminal circuit can be simplified to an equivalent circuit comprising a voltage source (Vth) in series with a resistance (Rth). Here, Vth is the open circuit voltage, and Rth is the equivalent resistance when all independent sources are turned off. The paragraph explains that the current (I) through the load resistor (RL) can be calculated using the formula: I = Vth / (Rth + RL). The initial steps involve finding Rth by turning off independent sources and calculating the parallel resistance between 6-ohm and 10-ohm resistors, resulting in 3.75 ohms.

05:01

🔍 Applying Kirchhoff's Voltage Law (KVL) to Calculate Current

This paragraph describes the application of Kirchhoff’s Voltage Law (KVL) to calculate the open circuit voltage (Vth) and the current through different loops. The KVL equation for the outer loop is set up, considering the voltage drops across each element, leading to a value of current I = 0.5A. Further, the same process is repeated for the inner loop to find the value of Vth, which comes out to be 17V. Finally, the paragraph concludes with the calculation of load current using the derived Vth and Rth values along with the given RL (8 ohms). The result is a current of 1.446A through the 8-ohm resistor, effectively demonstrating the use of Thevenin’s theorem in circuit analysis.

Keywords

💡Thevenin's Theorem

Thevenin's Theorem is a method used in circuit analysis, which simplifies a complex circuit into an equivalent circuit with a single voltage source (Vth) in series with a resistor (Rth). This equivalent circuit is used to calculate the current through a load resistor. In the script, Thevenin's Theorem is applied to find the current through an 8-ohm resistor.

💡Vth (Thevenin Voltage)

Vth is the open-circuit voltage across the terminals of the two-terminal linear circuit. It is part of the equivalent circuit in Thevenin's Theorem. In the video, Vth is calculated as 17 volts, which helps determine the current through the load resistor.

💡Rth (Thevenin Resistance)

Rth is the equivalent resistance of the circuit when all independent sources are turned off, and it is another component of the Thevenin equivalent circuit. In the video, Rth is calculated as 3.75 ohms, and this value is used along with Vth to compute the current.

💡Load Resistor (RL)

The load resistor (RL) is the resistor for which we want to find the current in a given circuit. In the context of Thevenin’s Theorem, the load resistor is removed during the calculation of Rth and Vth, and then added back to find the final current. In the video, the load resistor is given as 8 ohms.

💡KVL (Kirchhoff's Voltage Law)

KVL states that the sum of all voltages around any closed loop in a circuit is equal to zero. This law is used in the script to calculate the current in both the outer and inner loops of the circuit. KVL is applied to determine the voltage and current values needed for the Thevenin equivalent.

💡Independent Sources

Independent sources refer to voltage or current sources in a circuit that provide a fixed value of voltage or current. When calculating Rth, all independent sources are turned off (voltage sources are short-circuited, and current sources are opened). In the video, the voltage source is short-circuited to calculate Rth.

💡Parallel Resistors

When two resistors are connected in parallel, their equivalent resistance can be calculated using the formula R = (R1 * R2) / (R1 + R2). In the video, two resistors (6 ohms and 10 ohms) are in parallel, and their equivalent resistance is calculated as part of the process to find Rth.

💡Outer Loop

The outer loop in a circuit refers to the path through which current flows in the main part of the circuit. In the video, KVL is applied to the outer loop to determine the overall current in the circuit, which is needed for calculating Vth and the current through the load resistor.

💡Inner Loop

The inner loop is another closed path in the circuit, typically involving different components or branches. In the script, KVL is applied to the inner loop to further refine the current values, specifically calculating the Thevenin voltage (Vth) by solving equations based on the loop.

💡Current (I)

Current refers to the flow of electric charge in a circuit. In this video, the primary goal is to calculate the current through an 8-ohm resistor using Thevenin’s Theorem. The current is found to be approximately 1.446 A after calculating the values of Vth, Rth, and RL.

Highlights

To find the current through the 8 ohm resistance, apply Thevenin’s theorem.

Thevenin's theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source (Vth) in series with a resistor (Rth).

Vth is the open-circuit voltage at the terminals, and Rth is the equivalent resistance when all independent sources are turned off.

To calculate the current through the load resistor (RL), use the formula: I = Vth / (Rth + RL).

First, turn off all independent sources and remove the load resistor to find Rth.

In this circuit, the 6 ohm and 10 ohm resistors are in parallel, leading to an equivalent resistance (Rth) of 3.75 ohms.

Next, find the open-circuit voltage (Vth) by applying Kirchhoff’s Voltage Law (KVL) to the outer loop.

After applying KVL to the outer loop, the current I is found to be 0.5 amperes.

Apply KVL to the inner loop to find Vth, resulting in Vth = 17 volts.

With Rth = 3.75 ohms and Vth = 17 volts, the Thevenin equivalent circuit can be drawn.

The load resistor RL is given as 8 ohms.

Using the formula I = Vth / (Rth + RL), substitute values: I = 17 / (3.75 + 8).

The current through the 8 ohm resistor is calculated to be 1.446 amperes.

This method shows how to calculate current using Thevenin’s theorem.

The video provides step-by-step instructions, from turning off sources to applying KVL, to find current in a circuit.

Transcripts

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heavin theorem question find current

through 8 ohm resistance here in this

circuit we have to find the current

through this 8 ohm resistance by using

thin theorem

solution first of all we will see what

is thin

theorem thin theorem states that a

linear two terminal circuit can be

replaced by an equivalent circuit

consisting of a voltage source

vth in series with a resistor

rth where this vth is the open circuit

voltage at the terminals and this RT is

the equivalent resistance at the

terminals when all the independent

sources are turned off and this is the

load resistor

RL

this is load resistor RL and this is

current I load current I now we can

easily find the value of I I is equal to

vth / rth +

RL rth + RL and this circuit is called

as thin equivalent

circuit

heavin

equivalent

circuit

now first of all we will find the value

of

rth so to find

rth turn of all independent forces turn

of all

independent

sources now here we can see in this

circuit we have to find the value of rth

so first step is to turn off all the

independent

sources now when we turn off this

voltage source that time it will be

short circuited also we have to remove

here we can write and

remove remove remove RL so this is the

load registor RL we have to remove this

from here and now this will be our rth

that is thin

resistance so here we can write rth is

equal to here we can see this 6 ohm and

10 ohm are connected in parallel so it

will be 6 ohm parallel with 10

ohm now when we solve this so it will be

6 into

10 divided by 6 +

10 6 into 10 ID 6 +

10 so it is

3.75 3 75 is the value of rth since it

is resistance so its unit will be ohm

now next we have to find the value of

vth so to find

vth to find vth first of all

remove remove

RL

and V that is open circuit voltage is

equal to vth

let's copy this circuit once more

time now here we have to remove this RL

and now this will be the open circuit

voltage or we can directly write this

will be our vth this will be positive

here and negative here so here we have

to find this

voltage first of all we will apply kvl

to the outer loop let's say this current

is current

I let's say this is a

loop with current I so we will

apply

kvl to Outer Loop apply kvl to Outer

Loop now let's say according to the

direction of this current this will be

positive here negative here positive

negative let's say we are starting from

this point so it will be -

20 then + 6

I + 6 I then + 20 I + 10

I + 10 I then + 12 + 12 is equal to 0

here the loop is completed so the

algebraic sum of all the voltages in a

loop is equal to Z this is called as kvl

that is kiro's voltage law now we can

find the value of current I from this

equation so it will

be this - 20 and this + 12 this will be

- 8

and this will be + 16

I is equal to 0 so 16 I is equal to 8 so

I is equal to 8 by 16 it is equal to 1x

2 or we can write it is 0.5

ampere now we got the value of current I

again we will copy this circuit from

here and the value of I is

0.5 now we will apply kvl to Inner Loop

let's say this current is current

i1 so here we can write

apply kvl to Inner

Loop apply kvl to Inner Loop now let's

say we are starting from this point so

it will be -

20 then + 6 i1 + 6 6 i1 then plus

vth plus vth is equal to0 now here we

can see this current I is equal to i1 so

here we can write I is equal to i1 is

equal to 0.5 ampere ampere here so here

we can write -20 + 6 in place of i1 we

will write 0.5 then plus we V is equal

to Z so therefore vth is equal to this

will

be - 20 then + 6 into

0.5 so it is -7 if it goes on right side

so it will be + 17 Vol so this is the

value of vth now we got the value of vth

that is heavin voltage and heavin

resistance rth so we can draw thin

equivalent circuit so let's copy this

circuit from

here and now let's tast it here now

substitute the value of v it is 17

volt and the value of rth is 3.75

ohm so it is 3 75 ohm the value of RL

here we can see in this question we have

to find the current through 8 ohm

resistance that means this is our RL so

here we can write RL is equal to 8 ohm

or we can write it

here here RL is equal to 8

ohm so RL is equal to

8om now we have to find this

I the value of vth is

177 the value of rth is

3.75 plus the value of RL is 8 so this

will

be 17 ided

3.75 +

8 so it is 1.44 6

1.44 6 and since it is current so its

unit will be ampere so therefore I 8 ohm

is equal to i l is equal to 1. 446

aamp so this is how we can find the

value of current by using thein theorem

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watching