Norton's method
Meshes are inner loops.
This is a two-mesh circuit. The outer loop R1, R3, R4, R5 is not a mesh.
Since there are only two meshes and three branches it is going to be easier to use Norton's theorem rather than Thevenin's. At least that is my opinion.
B
Diagram
1
Step one.
Shift the earth to the bottom node, B.
The position of the earth doesn't effect the currents since there is no return path for the Earth connection. Therefore it won't affect the voltage drops across the resistors.
It will affect the voltages since these are referenced to earth but that is a simple matter to deal with at the end.
Diagram 2
Now the Norton method involving short circuiting both the sources.
Don't do this at home. In fact don't even do it a friends place when their parents are out. This is a mental exercise only unless you are very, very sure the resistors can take the extra currents involved.
Think of the 12 V
battery and R1 and R2 as one source and the 5 V battery with R3
and R4 as the other source.
Fortunately shorting out Rx achieves both these goals
simultaneously. See the next diagram.
Diagram 3
The 12 V battery gives 6 mA down the short circuit.
The 5 V battery gives 5/3.7 mA up the short circuit.
These short circuit currents are called Norton currents.
That gives a net current of 4.65 mA down the short circuit ie the total Norton current is 4.65 mA fed into the top node.
Diagram 4
The combined
resistance of the parallel paths is about 816
This develops
3.79 Volts between the top node labelled A and the bottom node labelled B. It is useful to note that
Now look back to diagram 2
By Kirchhoff's loop rule for voltages
Now look back to diagram 1
Every thing else is Ohm's
law.
Have fun and let me know how easy this is to read.
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