DC Network theorems Norton’s and Thevenin’s theorem

In summary, the conversation discusses a problem involving Norton's and Thevenin's theorems to determine power dissipation and maximum power transfer in a circuit with various resistances. The equations used and an attempt at a solution are provided, and the request for a schematic is made.
  • #1
steven1988
2
0
hi,
thanks for taking time to try and help me out, i have hit a brick wall with these questions, i have made an attempt and don't no where to go from there, and feed back would be great thanks alot...

The problem
Using both Norton’s and Thevenin’s theorem determine the power dissipated in the 4Ω resistance.

If the 4Ω resistance was removed calculate the value of load that will result in maximum power being transferred

Calculate the value of power transferred

the circuit has a:-
60 V supply
10Ω
10Ω
20Ω




1.5Ω


Homework Equations


I = V
Z
P= I^2R

The Attempt at a Solution


I = V
Z
= 60
58.5
= 1.02
P= I^2R
= 1.02^2 * 4
= 4.426 W
I = V
Z
= 60
54.5
1.10
P= I^2R
= 1.10^2 * 54.5
= 65.945 w
 
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  • #2
You should post a schematic of your problem.

It might be seen sooner if you upload to an image hosting site, and post the link here.
 
  • #3


Hi there,

DC Network theorems, such as Norton's and Thevenin's, are fundamental concepts in circuit analysis that allow us to simplify complex circuits into simpler equivalent circuits. Both theorems can be used to determine the voltage, current, and power in a specific part of a circuit.

In this problem, we are asked to determine the power dissipated in the 4Ω resistance using both Norton's and Thevenin's theorem. To do this, we first need to find the equivalent circuit for the given circuit.

Using Thevenin's theorem, we can find the Thevenin voltage (Vth) and Thevenin resistance (Rth) of the circuit. Vth is the open-circuit voltage at the terminals of the 4Ω resistance, while Rth is the equivalent resistance seen from the same terminals. Using the given values, we can calculate Vth and Rth as follows:

Vth = (10+10+20+5+5+4+2+1.5+1)Ω * 60V / (10+10+20+5+5+4+2+1.5+1)Ω = 60V
Rth = (10+10+20+5+5+4+2+1.5+1)Ω // (10+10+20+5+5+4+2+1.5+1)Ω = 1.02Ω

Now, using Norton's theorem, we can find the Norton current (In) and Norton resistance (Rn) of the circuit. In is the short-circuit current at the terminals of the 4Ω resistance, while Rn is the equivalent resistance seen from the same terminals. We can calculate In and Rn as follows:

In = 60V / (10+10+20+5+5+4+2+1.5+1)Ω = 1.02A
Rn = (10+10+20+5+5+4+2+1.5+1)Ω // (10+10+20+5+5+4+2+1.5+1)Ω = 1.10Ω

Now, using the equivalent circuit and Ohm's law, we can find the current flowing through the 4Ω resistance as:

I = V
 

What is Norton's theorem?

Norton's theorem states that any linear electrical network can be replaced by an equivalent current source and a single resistor connected in parallel. This equivalent circuit is called the Norton equivalent circuit. It is useful for simplifying complex circuits and analyzing the behavior of current in a network.

What is Thevenin's theorem?

Thevenin's theorem states that any linear electrical network can be replaced by an equivalent voltage source and a single resistor connected in series. This equivalent circuit is called the Thevenin equivalent circuit. It is useful for simplifying complex circuits and analyzing the behavior of voltage in a network.

What is the difference between Norton's and Thevenin's theorem?

The main difference between Norton's and Thevenin's theorem is the type of equivalent circuit they provide. Norton's theorem gives an equivalent current source and a parallel resistor, while Thevenin's theorem gives an equivalent voltage source and a series resistor. In other words, Norton's theorem is useful for analyzing current behavior, while Thevenin's theorem is useful for analyzing voltage behavior.

When should I use Norton's theorem versus Thevenin's theorem?

You should use Norton's theorem when you are interested in analyzing the current behavior of a circuit. This is useful for calculating power dissipation, voltage drops, and other current-related characteristics. On the other hand, you should use Thevenin's theorem when you are interested in analyzing the voltage behavior of a circuit. This is useful for calculating voltage drops, power supply requirements, and other voltage-related characteristics.

Are Norton's and Thevenin's theorem applicable to all types of circuits?

Yes, Norton's and Thevenin's theorem are applicable to all types of linear electrical circuits, including DC circuits. However, these theorems may not be applicable to non-linear circuits, such as those containing diodes or transistors.

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