The problem asks to solve for V1, V2, V3, and V4 I am curious as to why the cheg

Question

The problem asks to solve for V1, V2, V3, and V4

I am curious as to why the chegg expert did not identify V2 and V3 as a supernode since they are both between a voltage source.

Because he ended up doing KCL at V3 instead of the supernode like so:

However, I used V2 and V3 as the supernode and doing KCL ended up with:

(V2 - V1)/10 + (V3-V4)/20 - 2 = 0

(1/10)V2 + (1/10)V3 - (1/20)V4 = 4.5 [V4 = Va]

2V2 + 2V3 - V4 = 90

Everything else I got correct expect when he applied KCL at V3 and I applied it at the supernode.

So because of that, we ended up getting different voltages for V1, V2, V3, V4

Did I do something wrong or is it not a supernode?

The problem asks to solve for V1, V2, V3, and V4 I am curious as to why the chegg expert did not identify V2 and V3 as a supernode since they are both between a voltage source. Because he ended up doing KCL at V3 instead of the supernode like so: However, I used V2 and V3 as the supernode and doing KCL ended up with: (V2 - V1)/10 + (V3-V4)/20 - 2 = 0 (1/10)V2 + (1/10)V3 - (1/20)V4 = 4.5 [V4 = Va] 2V2 + 2V3 - V4 = 90 Everything else I got correct expect when he applied KCL at V3 and I applied it at the supernode. So because of that, we ended up getting different voltages for V1, V2, V3, V4 Did I do something wrong or is it not a supernode?

Explanation / Answer

Voltage V2 is not a super node . It is not a supernode as the voltage at V2 is 0. So u cannot find the voltage considering V2 as it will disturb the equation.

Suppose any of the branches in the network has a voltage source then it is slightly difficult to apply nodal analysis .One way to overcome this difficulty is to apply the Supernodal technique.

The above condition is not satisfying in your question so it is not considered as a supernode

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