Understanding KVL and Voltage Differences

[teh_cookie]

Homework Statement

Homework Equations

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

The Attempt at a Solution

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?

 

[anthonuc]

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.

 

[CEL]

Your solution is correct. Your professor made a mistake.

 

[teh_cookie]

thanks for the help! i just got an email and it was a typo and the answer is -3

 

[DeeNos]

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.