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Theoretical foundations of electrical engineering

Equivalent generator method, solution example

Given
Е1=9 V;
Е2=13 V;
Е3=15 V;
J=1,4 А;
R1=12 ohms;
R2=16 ohms;
R3=9 ohms;
R4=5 ohms;
R5=10 ohms.
Find
Current on the R2 resistor by the equivalent generator method:

Solution

Equivalent generator method

According to the theorem of the equivalent generator the load current can be found by formula:
Equivalent generator method

Uхх — voltage of the generator no-load;
Rн — load impedance;
Rг — generator impedance concerning load terminals.

We find the generator impedance and voltage of the no-load. In calculating the equivalent resistance, we notice that the EMF source impedance is equal zero and resistance of the current source is infinite. Construct a diagram of the equivalent generator:
Equivalent generator method

and diagram for finding resistance:

Calculation using Equivalent generator method

Calculation using Equivalent generator method
Ответ: I2=-0,076 А.

The current through R2 resistor found by the node potential method coincides with the calculated above that confirms the correctness of the solution.
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