# Calculating Norton Equivalent Circuit for Complex Load Impedance

• Engineering
• Joe85
In summary, the conversation discusses the conversion of V1 and V2 to RMS values and the calculation of load voltage and current using Ohm's Law. The circuit is redrawn several times and the load impedance is replaced with a short circuit or placed back into the circuit. The final result is an identical calculation to the original method used.
Joe85
Homework Statement
Hi all,

I realise that this question has been asked numerous times in relation to Parts A and B but am strugging to find any ground covered on Part C. I believe i have answered this correctly but the wording of the question leads me to believe perhaps i have missinterpreted what was being asked.

The Question:

FIGURE 1 shows a 50 Ω load being fed from two voltage sources via
their associated reactances. Determine the current i flowing in the load by:

(a) applying Thévenin’s theorem
(b) applying the superposition theorem
(c) by transforming the two voltage sources and their associated
reactances into current sources (and thus form a pair of Norton
generators)

Relevant Equations
.

V1 = 415cos(100πt)
V2 = 415sin(100πt)
Load Impedance = 50Ω (0.7 Pf Lag) = 35.002 + J35.705Ω
Converting V1 & V2 to RMS values and V1 to a sin value:
V1 = 415cos(100πt)
V2 = 415cos(100πt-90)
and from Asin(ωt+Φ)
V1 = 415∠0V or 415 +J0V
V2 = 415∠-90V or 0-j415 VIntially, i convert the the volage sources into current sources:

I1 = V1/J4 = -J103.75A
I2 = V2/J6 = -69.16666667A

I then red-draw the circuit with the voltage sources replaced with current sources and the series impedances placed in parallel with the current source.

Next step was to remove the load impedance and replace with a short circuit. I then took the current through the Short Circuit (Points A & B):

Isc = I1+I2 = -69.16666667 - J103.75A.Next step was to replace the the current sources with Open Circuits and remove the short circuit that was placed beween Points A & B.

With the Two Reactances in parallel:

Zn = (Z1Z2)/(Z1+Z2)
Zn = J2.4ΩCircuit is now redrawn as a Norton Equvalent with Isc in parallel with Zn and an open circuit between Points A & B.

Once again, redrew the circuit again placing the Load (ZL) back into the circuit between points A & B.

Zn & Zl now in parallel - Product over sum rule to reduce to a total impedance Zt:

Zt = (ZnZL)/(Zn+ZL) = 0.07530879804 + J2.318014921Ω

Calculated the Load Voltage using Ohms Law:

VL = Isc × Zt = 235.2851896 - J168.1426532.Finally, i calculated the load current utilising Ohms Law on Load impedance:

IL = VL/ZL = 0.8927 -J5.714A.The answer is identical to my answer for parts A & B (to 4 sf - may revist the calculations to tidy up), just not sure the method I've used is what they were asking.

Thanks,

Joe.

That looks like how I'd do it, if asked to make a Norton equivalent.

Joe85
Thank you for the response, Scott.

## 1. What is a Norton generator?

A Norton generator is a type of electric generator that is used to convert mechanical energy into electrical energy. It is named after its inventor, American physicist Edward L. Norton.

## 2. How does a Norton generator work?

A Norton generator works by using a rotating magnetic field to induce an electric current in a set of stationary coils. This current is then collected and sent through wires to power devices or appliances.

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

Norton generators have several benefits, including their simplicity and efficiency in converting mechanical energy into electrical energy. They are also compact and portable, making them useful in a variety of settings.

## 4. Can Norton generators be used for renewable energy sources?

Yes, Norton generators can be used for renewable energy sources such as wind turbines and hydroelectric power. They can also be used in conjunction with solar panels to store excess energy.

## 5. How do I choose the right size Norton generator for my needs?

The size of a Norton generator is typically determined by the amount of power it can produce, measured in watts. To choose the right size, consider the wattage requirements of the devices or appliances you want to power, and select a generator with a slightly higher wattage capacity.

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