# How Do You Calculate Norton Equivalent Circuits in Electrical Engineering?

• Engineering
• ihavaquestion
In summary, to find the Norton equivalent circuit, one can use mesh analysis or superposition to calculate the current in ab. The total current will be the sum of two partial currents. Alternatively, using superposition, the problem can be solved by dealing with current dividers.
ihavaquestion

## Homework Statement

Find norton equivalent circuit

Rn=Rth

## The Attempt at a Solution

Ok i got my R(n)=34 ohms because after you turn off independent sources the resistors are in series, then I short circuited a to be and I'm trying to use mesh analysis to solve for I(n)
the problem arises with the 2 amp current source does that make I2 and I3 2 amps? help!?

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ihavaquestion said:

## Homework Statement

Find norton equivalent circuit

Rn=Rth

## The Attempt at a Solution

Ok i got my R(n)=34 ohms because after you turn off independent sources the resistors are in series, then I short circuited a to be and I'm trying to use mesh analysis to solve for I(n)
the problem arises with the 2 amp current source does that make I2 and I3 2 amps? help!?

You can write the mesh equations for the circuit and calculate the current in ab.
Or you can use superposition: cancel one of the current sources and calculate the current, then activate that source and cancel the other. The total sum of the two partial currents. current is the

ihavaquestion said:
the problem arises with the 2 amp current source does that make I2 and I3 2 amps? help!?

You didn't label the diagram with mesh currents, so I'll guess that you have three meshes numbered from left to right in the circuit. For clockwise mesh currents i1, i2, i3, the 2A independent source will make i3 - i2 = 2A.

Note that you could also solve the problem pretty easily using superposition: you get a couple of straightforward current dividers to deal with.

The Norton equivalent circuit is a useful tool in simplifying complex circuits and analyzing their behavior. It is important to note that the Norton equivalent circuit is only valid for linear circuits, where the relationship between current and voltage follows Ohm's law.

In order to find the Norton equivalent circuit, we first need to find the equivalent resistance (Rn) of the circuit. This can be done by turning off all independent sources and calculating the resistance of the circuit. In this case, the equivalent resistance is 34 ohms.

Next, we need to find the current source (In) of the Norton equivalent circuit. This can be done by short-circuiting the output terminals and solving for the current flowing through the short circuit. In this case, the current source is 2 amps.

The Norton equivalent circuit is then represented as a current source (In) in parallel with the equivalent resistance (Rn). This equivalent circuit behaves the same as the original circuit, with the same voltage-current relationship at the output terminals.

In order to use mesh analysis, you can consider the 2 amp current source as a superposition of two independent sources - a 2 amp current source and a 0 volt voltage source. This will allow you to solve for the mesh currents (I2 and I3) and then use the superposition principle to find the total current (In) of the Norton equivalent circuit. Alternatively, you can also use Thevenin's theorem to convert the circuit to its Thevenin equivalent and use mesh analysis from there.

I hope this helps! Remember, it's always important to double check your calculations and make sure you have a good understanding of the concepts before moving on to more complex analysis techniques.

## 1. What is a Norton equivalent circuit?

A Norton equivalent circuit is a simplified representation of a complex electrical circuit that is used to analyze and solve problems. It consists of a current source in parallel with a resistor, and it can be used to calculate the behavior of the original circuit in terms of current and resistance.

## 2. How is a Norton equivalent circuit different from a Thevenin equivalent circuit?

A Norton equivalent circuit is mathematically equivalent to a Thevenin equivalent circuit, but it is represented in terms of a current source instead of a voltage source. In other words, a Norton equivalent circuit represents a circuit's behavior in terms of current, while a Thevenin equivalent circuit represents it in terms of voltage.

## 3. What are the benefits of using a Norton equivalent circuit?

A Norton equivalent circuit can simplify complex circuits and make them easier to analyze. It can also help in determining the maximum power that can be delivered to a load, and it can be used to compare different circuit configurations and choose the most efficient one.

## 4. How do you calculate the Norton equivalent current and resistance?

To calculate the Norton equivalent current, you need to short-circuit the original circuit and measure the current flowing through the short circuit. This current will be the Norton equivalent current. To calculate the Norton equivalent resistance, you need to replace all the independent voltage sources in the original circuit with short circuits and all the independent current sources with open circuits. Then, you can calculate the equivalent resistance using the same methods as for a Thevenin equivalent circuit.

## 5. Can a Norton equivalent circuit be used with AC circuits?

Yes, a Norton equivalent circuit can be used with AC circuits, but the values of the current source and resistance will vary with frequency. The calculation of the equivalent current and resistance will also be different for AC circuits, taking into account the impedance of the circuit components.

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