Some known facts: v2 - v1 = 10 v3 - v2 = Va v3 = 5Va I applied KCL @ supernode (

Question

Some known facts:

v2 - v1 = 10

v3 - v2 = Va

v3 = 5Va

I applied KCL @ supernode (v1 & v2):

(1/10)v1 + (1/2)v2 - (1/2)v3 = 0

I applied KCL @ v3:

(v3-v2)/2 + 5Va + (v3-10)/30 = 0

(v3-v2)/2 + 5(v3 - v2) + (v3-10)/30 = 0 [since v3 - v2 = Va]

-(11/2)v2 + (83/15)v3 = 1/3

Using:

v2 - v1 = 10

(1/10)v1 + (1/2)v2 - (1/2)v3 = 0

-(11/2)v2 + (83/15)v3 = 1/3

I put it in a matrix, and ended up with:

v1 = 3x10^-13 V

v2 = 10 V

v3 = 10 V

However, CHEGG answers has:

v1 = -50 V

v2 = -40 V

v3 = -50 V

So can someone please tell me what I did wrong?

It would be nice if you can solve it yourself and post a picture of it on here.

Its really difficult to read it on here if its typed :)

Thanks

Some known facts: v2 - v1 = 10 v3 - v2 = Va v3 = 5Va I applied KCL @ supernode (v1 & v2): (1/10)v1 + (1/2)v2 - (1/2)v3 = 0 I applied KCL @ v3: (v3-v2)/2 + 5Va + (v3-10)/30 = 0 (v3-v2)/2 + 5(v3 - v2) + (v3-10)/30 = 0 [since v3 - v2 = Va] -(11/2)v2 + (83/15)v3 = 1/3 Using: v2 - v1 = 10 (1/10)v1 + (1/2)v2 - (1/2)v3 = 0 -(11/2)v2 + (83/15)v3 = 1/3 I put it in a matrix, and ended up with: v1 = 3x10^-13 V v2 = 10 V v3 = 10 V However, CHEGG answers has: v1 = -50 V v2 = -40 V v3 = -50 V So can someone please tell me what I did wrong? It would be nice if you can solve it yourself and post a picture of it on here. Its really difficult to read it on here if its typed :)

Explanation / Answer

Some known facts: v2 - v1 = 10 v3 - v2 = Va v3 = 5Va I applied KCL @ supernode (v1 & v2): (1/10)v1 + (1/2)v2 - (1/2)v3 = 0 I applied KCL @ v3: (v3-v2)/2 + 5Va + (v3-10)/30 = 0 ....... This is the wrong step.... U are applying KCL here. U are supposed to add all currents at node V3. But U have added 5Va in the equation which is a voltage not a current. So, this equation is wrong. Right steps: In fact, u don't need to apply KCL at node V3. From the 3 equations in the known facts, u will get V1, V2, V3 in terms of Va. Substitute V1, V2 and V3 in the KCL equation at Supernode (V1&V2) Now, u will get a equation in which the only unknown is Va. Find Va. Substitute Va value in the V1, V2 and V3 equations. (As we know V1, V2 and V3 all in terms of Va only). U will get the right answers which would be equal to CHEGG answers.

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