From our previous discussion of Nodal Analysis we have seen,
how voltage sources affect nodal analysis. We have also seen how a voltage
source makes it easier for us to calculate the node voltages when connected
with a reference node. But things get complicated when a voltage source cannot
be referenced i.e. it comes in between two non-reference node. This voltage
source along with two non-reference nodes forms a supernode.
In summary, When a voltage source comes in between two
non-reference node then these two non-reference nodes and the voltage source
form a supernode and we take this supernode as a single node and apply KCL and
KVL to solve the circuit.
To solve a problem of supernode follow these steps:
01.
Mark a reference node such
that a supernode can’t be formed. Try to avoid supernode at first hand. If it’s
not possible then at least make a voltage source referenced.
02.
Then mark other
non-referenced nodes as you do in normal nodal analysis.
03.
Next, mark the supernode
with a dotted circle to remind you that it’s a supernode.
04.
Now apply KCL at the
supernode.
05.
At the end apply KVL at the
supernode loop to find the node voltages in supernode.
Let us explain this procedure with an example:
First of all we have marked a reference node V0. Then we
marked all other nodes as we do normally for nodal analysis.
Now we have given a dotted circle to remind us that this is
a supernode along with V1 and V2.
Now we apply KCL at the circuit:
2 = (V1 – 0) / 2 + (V2 – 0) / 4 +7
8 = 2 V1 + V2 +28 (multiplying both sides by 4)
2 V1 + V2 = -20 ………………………………………………. (a)
Now we apply KVL at the supernode loop:
-V1 - 2 +V2 = 0
V2 = V1 + 2 ……………………………………………………. (b)
Putting this value of V2 in equation (a):
2 V1 + (V1 + 2) = -20
3 V1 = -22
V1 = -22/3 V
Now from (b): V2 = -22/3 +2 = -16/3V
Note that the 10 Ohm resistor connected across the supernode
does not make any difference in the calculations as it is connected across the
supernode.
Excellent lecture about supernode
ReplyDeleteslam.
Deletesir it is really good xplanation
i need some more difficult problems that covers all about supernode.
zeeshan
xee_raza@yahoo.com
Excellent work you have a great future ahead of you
Deletenice... i also wanna get more complicated ones
ReplyDeleteExcellent work...
ReplyDeleteEasy to understand...
I completed my class assignment..
i need more difficult problem.
ReplyDeletethanq u sir
ReplyDeletebecoz of u only i completed my assignment
what will happen if we replace the 10 Ohm resistor with 10Amp????
ReplyDeletepractically that is not possible,
Deletea 10 Amp source means that current flowing across two nodes is 10 Amps, and
a 2 V source means that a potential difference of two volts is present across two nodes,.........
now, if you are saying that current entering one node is 10 amp and that leaving it is also 10 Amp, so technically there is no potential difference across the two nodes but a voltage source means that there is a potential difference of 2V across the two points,..........
and this will result in a conflict,..............
so, physically such a situation will not be possible
Good answer
DeleteWell, let just hope i won't go through it tomorrow,,
ReplyDeletecan u explain more detail about the calculation?
ReplyDeletewhat if there are three nodes (say v1, v2 & v3) with two voltage a sources one between v1 & v2 and the other between v2&v3? Can we take three nodes in a super node?
ReplyDeleteI Do It My Self Using Super Node Its Good And Your Method Same As Me
ReplyDeleteGood Work😊
Got a clear understanding of it from here. Had a difficult time understanding my teacher in class yesterday. Good work
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