Network Theory Problem do help

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The discussion revolves around solving a network theory problem involving voltage and current in a circuit with various resistors and voltage sources. The user initially attempted to use Kirchhoff's Current Law (KCL) and nodal analysis but found the equations complex. They concluded that the voltage difference Vc - Vd equals -5 volts based on their calculations. Other participants confirmed the reasoning and results as correct, suggesting that alternative methods would ultimately yield similar conclusions. The consensus is that while different approaches can be explored, they may lead to the same mathematical results.
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1. Homework Statement
Va - Vb = 6 Volts
Calculate Vc - Vd = ?
The circuit diagram is shown below :-

All resistances are equal to "R" as shown in fig. except for 1 ohm and 2 ohm resisters.
Two voltage sources 10V and 5V are given and a current source in parallel to 1 ohm resistor.

Homework Equations


3. The Attempt at a Solution :
I thought of using KCl and nodal analysis method but the equations became quite complex.
Though i thought that the current flowing through 2 ohm resistor will be equal to current flowing in branch connecting Vc and Vd that will be 3 ampere using KCL.
Thus using kcl at node "M" current through 1 ohm resistor will be 5 ampere and thus voltage drop equals "5 volts = Vd - Vc". Therefore Vc - Vd equals -5 volts.

Am i doing it right and is there any other method to solve this question ?
 

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Your reasoning and results are both correct. Well done.
 
Thanks. But is there any other method to solve this problem ?
 
lazyaditya said:
Thanks. But is there any other method to solve this problem ?

Well, even if you simplified the left and right portions of the network and wrote KVL and KCL equations, it would probably boil down (mathematically) to the same thing -- things would cancel here and there to leave you to draw the same conclusions.
 
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