thevenin's theorem explanation | Thevenin's Theorem Solved Example Problem
Summary
TLDRThis 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
🔧 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.
🔍 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.
Mindmap
Keywords
💡Thevenin's Theorem
💡Vth (Thevenin Voltage)
💡Rth (Thevenin Resistance)
💡Load Resistor (RL)
💡KVL (Kirchhoff's Voltage Law)
💡Independent Sources
💡Parallel Resistors
💡Outer Loop
💡Inner Loop
💡Current (I)
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
to get the free notes of electrical
circuits check the link in the comment
section and install the app for free
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
check the link in the comment section
and install the app for free to get the
notes of electrical circuits thanks for
watching
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