# How to get the unknown variables through voltage division?

Given this circuit, how do I find E, Vz, and Vy when Vx is 3V?

When I tried solving it, through simplification of circuits, (correct me if I'm wrong) I got a total resistance of 12k while resistance of Vy is 10k. Upon getting the total resistance, I used the voltage division formula to get E, since the formula is Vx = E(Rx/Rt) where E is the voltage source, Rx is the resistance of x and Rt is the total resistance, I manipulated it to get E, which, in my calculations, is 2.4V. Now this is where I'm confused, since E, which is the source, is less than the voltage of a resistor, did I make a mistake in my calculations? Since, from my understanding, a voltage source's voltage is always greater than the voltage of its elements? Also, can I solve it in the manner of finding Vy first, then Vz, then E? If so, how?

I manipulated it to get E, which, in my calculations, is 2.4V

That's incorrect so, just work from right to left filling out the details as you go: -

No need for any extensive analysis other than using ohm's law and writing things down.

I'm not providing a full answer, just a partial answer so you can see the method.

• is there any way to answer it with voltage division though? im trying to learn the concept and i think solving it that way would make me understand this types of problems more Mar 19 '21 at 11:50
• @AedenSchmidt sure there is. $V_{OUT} = V_{Y}\cdot\dfrac{6k}{6k+4k}$. Just rearrange to get Vy = 5 volts. Mar 19 '21 at 12:00
• @Aeden You can if you want to (and if you perform the calculations correctly) but the method shown by Andy is simpler. I suggest finish solving the problem using the method above. If you want to practice using voltage dividers do it again using that method and check your answers match those obtained using the method shown above. As your known voltage is on the right you'll need to work from the right progressively working out Vy, Vz and then E. Don't try to go from Vx to E in one go because it's very easy to introduce an error in a large expression (and you need to state Vy and Vz anyway). Mar 19 '21 at 12:23
• This answer isn't good. Mar 19 '21 at 14:36
• @MissMulan - If you believe an answer isn't good enough to upvote it, then don't upvote it. However please note the "green tick" next to the answer - that means that the OP found the answer was good enough to solve their problem & they accepted the answer. It is fine if you disagree with the OP - it would help if you explain why. Note that site policy here, currently being discussed on Meta, is that full homework answers tend to be discouraged. Helping to show an OP the process of solving their question (e.g. by socratic questions, hints & other methods) leads to them learning more. Thanks. Mar 19 '21 at 15:59

E=15v
My full solution is here:

• Please don't hand out solutions to obvious homework problems. We don't do that here. Mar 19 '21 at 14:52
• He asked. I gave the answer.yes my own. Mar 19 '21 at 15:44
• I think if some one try to learn from websites is great. Mar 19 '21 at 15:51
• @upali - Hi, "Some one half answerd" Yes, deliberately. "it was commented "this answer not good"" That comment is an opinion. Please see my comment above where I try to explain that, although the site community here is still discussing this, the general view is that full answers to homework tend to be discouraged. Even if the OP here did their research (and here, they did!) future readers can just copy & paste a full answer, without knowledge. Mar 19 '21 at 16:11
• @upali note that I didn't half-answer through laziness or incompetence; I half answered because the question was homework and this site doesn't give full answers to homework. If you downvoted my answer because of this, please reconsider this action because it is contrary to site customs. Mar 19 '21 at 18:20