Simple Nodal Analysis Problem Solution and Explanation

[Magnawolf]

Homework Statement

Homework Equations

KVL and KCL

The Attempt at a Solution

Let V = V1 and the Voltage across the 2 ohm resistor be V2 just for reference.

Step 1: KCL @ Supernode: V1/3 + V2/2 + 21/4 + V3/6 = 0

I think my problem is here somewhere. Does V3 = V2 because they're in parallel? Also, am I wrong to say that 21/4 is a current going out of the supernode?

Step 2: V2-V1 = 9 (pretty sure this is right)

I can't get the correct answer. Any help is appreciated.

 

[gneill]

Homework Statement

Homework Equations

KVL and KCL

The Attempt at a Solution

Let V = V1 and the Voltage across the 2 ohm resistor be V2 just for reference.

Step 1: KCL @ Supernode: V1/3 + V2/2 + 21/4 + V3/6 = 0

I think my problem is here somewhere. Does V3 = V2 because they're in parallel? Also, am I wrong to say that 21/4 is a current going out of the supernode?

Step 2: V2-V1 = 9 (pretty sure this is right)

I can't get the correct answer. Any help is appreciated.

The 2 and 6 Ohm resistors are in parallel so they must share the same potential difference. If V1 is the potential at the top of the 3 Ohm resistor then the potential difference across the 4 Ohm resistor must be V1 - 21.

If you make a supernode of the nodes either side of the 9 V source, then really you need only one voltage variable to write the equation. Suppose you chose v to be that variable (after all it's already specified in the circuit diagram). Then on one side of the source the potential is v and on the other side it's v+9. No need to introduce V2 or V3 etc.

 

[NascentOxygen]

Hi. Your V3 is V2, it's the one and the same node. Keep it as just V2.

The current through the 4Ω is given by (voltage across the 4Ω resistor itself) / 4

So what is the voltage across that 4 ohm resistor? Hint: the expression will involve a subtraction

 

[Magnawolf]

If V1 is the potential at the top of the 3 Ohm resistor then the potential difference across the 4 Ohm resistor must be V1 - 21.

This. This is what I needed. Thanks so much!

 

[rezeew]

Your approach to solving this nodal analysis problem is correct. However, there are a few mistakes in your equations that are leading to an incorrect answer. Let's break down your solution step by step and address the errors.

Step 1: KCL @ Supernode: V1/3 + V2/2 + 21/4 + V3/6 = 0

Your equation for the supernode is correct, but you have made a mistake in identifying the currents. V3 is not equal to V2 because they are in parallel. Instead, the current going through the 21 ohm resistor is equal to (V2-V3)/21. Also, the current going through the 2 ohm resistor is equal to V2/2, not V2 as you have written. Finally, the current going through the 4 ohm resistor is equal to (V1-0)/4, as there is no voltage drop across the ground node.

Step 2: V2-V1 = 9

This equation is also correct, as it is simply applying KVL around the outer loop of the circuit. However, you need to substitute the correct values for V1 and V2 in order to solve for the correct answer.

In summary, your approach to solving this problem is correct, but you have made some mistakes in identifying the currents and substituting the appropriate values in your equations. By correcting these errors, you should be able to arrive at the correct solution. Keep practicing and don't hesitate to ask for help if you get stuck on a problem. Good luck!