Network Theory Problem do help

[lazyaditya]

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 ?

 

[gneill]

Your reasoning and results are both correct. Well done.

 

[lazyaditya]

Thanks. But is there any other method to solve this problem ?

 

[gneill]

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.

 

[asteriatic]

Your attempt at solving this problem using KCl and nodal analysis is a valid approach. However, there are other methods that can be used to solve this problem as well. One alternative method could be to use Kirchhoff's voltage law (KVL) to analyze the circuit. KVL states that the sum of all the voltage drops in a closed loop must equal the sum of all the voltage sources in the loop. This law can be applied to any closed loop in the circuit, including the loop containing Vc and Vd.

Using KVL, we can write the following equation:
Vc - Vd - 5V - 10V - 1ohm * 3A = 0
Simplifying this equation, we get:
Vc - Vd = 6V
This is the same result that you obtained using KCl and nodal analysis.

In terms of whether your solution is correct, it is difficult to say without seeing your calculations. However, your approach and reasoning seem to be correct. It is always a good idea to double check your calculations and make sure they are accurate. Additionally, you can try solving the problem using different methods to verify your answer. If you get the same result using different methods, then it is likely that your solution is correct.