Understanding KVL and Voltage Differences

In summary, Vx is the difference of the bottom node to the right node and with KVL, the sum of all voltages around a loop equal 0. The equation for node analysis is (3-Vx)/3 - 2 = 0 and it solves for Vx = -3. The correct answer is -3 and the answer posted by the professor, -9, was a typo.
  • #1
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Homework Statement


eceKVL.jpg

Homework Equations


KVL, the sum of all voltages around a loop equal 0

The Attempt at a Solution


eceKVLsol.jpg


Vx is just the difference of the bottom node to the right node. With KVL I just add up the the voltage differences in a loop and equal to zero right? -15+12+6+Vx=0 Vx = -3 ... However my professor posted the answer and Vx = -9 ... why is that? what am I doing wrong?
 
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  • #2
Not sure I never use KCL/KVL anymore lol.

If you know how to use node analysis you can get the answer more quickly and easily.

Establish a node as ground and the voltage at the node you want to solve you just sum the currents into that node to zero.

Establishing the right node as ground:

node analysis equation:

(3-Vx)/3 - 2 = 0

Which solves for Vx = -3

I actually ended up with the same answer as you, perhaps you should ask your professor if it's a typo?

I could've solved it incorrectly as well though.
 
  • #3
Your solution is correct. Your professor made a mistake.
 
  • #4
thanks for the help! i just got an email and it was a typo and the answer is -3
 
  • #5


Your understanding of KVL is correct. The sum of all voltages around a closed loop must equal 0. However, it seems that in your attempt at a solution, you have not correctly accounted for the direction and signs of the voltages.

Firstly, it is important to establish a consistent direction for the loop. Let's say we start at the bottom node and move clockwise around the loop.

Next, we need to assign signs to the voltages. Since we are moving in a clockwise direction, we assign a positive sign to the voltages that we encounter as we move in that direction. Therefore, -15V and +12V are correctly represented in your attempt at the solution. However, when we reach the 6V source, we encounter it in the opposite direction (since we are moving clockwise) and therefore it should be assigned a negative sign. This means that the correct equation should be -15V + 12V - 6V + Vx = 0.

Solving for Vx, we get Vx = 9V. This means that the voltage difference between the bottom and right nodes is 9V, not -9V. It is important to pay attention to the direction and signs of the voltages when applying KVL.
 

1. What is KVL and why is it important in understanding voltage differences?

KVL stands for Kirchhoff's Voltage Law, which states that the sum of all voltages in a closed loop must equal zero. This means that the voltage drop across all components in a circuit must equal the voltage source. Understanding KVL is important because it helps to accurately predict and analyze voltage differences in a circuit.

2. How do you apply KVL to a circuit?

To apply KVL to a circuit, you must first identify a closed loop or path in the circuit. Then, starting at any point in the loop, assign a direction to the current flow and assign a positive or negative sign to each voltage drop based on the direction of the current flow. Finally, add all the voltage drops together and set the sum equal to zero.

3. Can KVL be applied to both series and parallel circuits?

Yes, KVL can be applied to both series and parallel circuits. In a series circuit, the voltage drops across each component will add up to the voltage source. In a parallel circuit, the voltage drops across each individual branch will add up to the voltage source.

4. How does KVL relate to Ohm's Law?

KVL and Ohm's Law are both fundamental laws in electrical circuits. Ohm's Law states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. KVL can be used in conjunction with Ohm's Law to solve for unknown voltages or currents in a circuit.

5. What are some common mistakes when applying KVL?

Some common mistakes when applying KVL include forgetting to include all voltage drops in a closed loop, not properly assigning positive and negative signs to voltage drops, and not setting the sum equal to zero. It is important to double check your work and make sure all components and their corresponding voltage drops are accounted for in the loop.

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