Norton Theorem Example # 2: Norton Equivalent for a Circuit with two Input Voltages

Statement: An Electrical network contains two voltage sources of 10 V and 20 V, and three resistors 5 k, 25 k and 15 k powering the load resistance. Find the Norton equivalent circuit.
 
Note: Before solving this problem you should have a basic knowledge about:

Solution:

Step 1: Remove the load resistor and mention the terminals. Here label 'ab' is used.

Step 2: Find the equivalent resistance at 'ab' terminals:
Step 3: Now apply the superposition principle to find the current passing through ab.

Step 3a: For 10 V source.
Remove the 20 V source and convert 10 V source to an equivalent circuit. The final circuit which we achieve is a 2 mA current source in series with three resistors, By applying current divider we achieve:

Step 3 b: Now for 20 V source, remove the 10 V input and apply the Ohm's law. Finally, a current source of 1.33 mA joins the three resistors. (Same circuit as above)
By applying KCL we get the current 0.173 mA.

Step 4: Final Norton Equivalent
Finally, add 0.173 mA to 0.260 mA and we achieve a 433 µA current source which connects parallel to the 28.75 kΩ resistance.


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