Can we do supernode questions by using only nodal analysis?

• Answer is YES.

➝ If we don't know about super node then we used simple node equation to solve any network contain super node.

• Before understanding this concept first we need to understand basics of Practical voltage source and Ideal Voltage Source:-

✱Practical Voltage Source:

➝ Voltage source in series with Internal Impedance (Zin) is referred as practical voltage Source.

➝Value of this internal Impedance is as low as possible,  Because if the value of Zin is high then Voltage drop across Zin is also high so voltage at load point or Terminal is Low. So it is required to choose the value of Zin is as low as possible.

Fig (a) Practical voltage source

✱ Ideal Voltage Source:

➝ Internal Impedance Zin of any practical voltage source is tends to ZERO is referred as Ideal Voltage Source.

➝It is important to know that "CURRENT OF ANY IDEAL VOLTAGE SOURCE IS NOT ZERO" , Because resistance of any ideal voltage source is tends to Zero not exactly Zero so that CURRENT  through the source is tends to Infinite, It means  Ideal Voltage Source is capable to deliver unlimited power.

Fib(b) Ideal Voltage Source

➡️ Consider the Network as shown in below figure, Find the Value of Vp_____& Vq_______in Volts Without using concept of SUPER NODE.

In this above network 5V source is Ideal Voltage Source so we assume current of an Ideal voltage source is "I". Direction of this current is assuming Negative terminal to Positive Terminal ( because current is always flow from Higher potential to lower potential).

• Applying Simple Node equation at Node Vp..............

       Vp-10/1 + Vp/2 - I =0 .............(1)

• Applying Simple Node equation at Node Vq.....,.......

       Vq/3 + Vq-10/4 + I =0 ..............(2)

➝Adding equation number (1)&(2).............

At that time "I" will be canceled out Please observed in equation.........

After adding equation number (1)&(2).........

   Vp-10/1 + Vp/2 + Vq/3 + Vq-10/4 = 0 ........(3)

Please observed equation number (3) is Same as Super Node equation......

      Vp- Vq = 5 .............(4)

Now find out Vp and Vq from Equation Number (3) & (4)............

Multiply by 12 in Equation Number (3)........

12Vp - 120 + 6Vp + 4Vq + 3Vq - 30 =0

Simplified........

18Vp + 7Vq =150 .............(5)

Now multiply 7 in Equation Number (4).........

7Vp - 7Vq = 35 ............(6)

Adding equation number (5)&(6)...........

After adding we get 

        25Vp = 185

∴ Vp = 7.4 Volt

Put value of Vp in equation Number (4.).....

            5 = Vp - Vq

        ∴ Vq = 7.4 - 5

           Vq = 2.4 Volt

So without using concept of SUPER NODE we can easily solving Any questions.

          ...............Thank you 🙂...............