How Do Current and Voltage Divide in Different Branches of a Circuit?

AI Thread Summary
In the discussion about current and voltage division in a circuit, the focus is on solving for the current in each branch given a resistor and voltage source. The equations used include a loop equation for both the left and right loops, with participants clarifying the significance of current direction and sign conventions. It is emphasized that the direction of current arrows is arbitrary, and incorrect assumptions about current flow can lead to negative values, which are still valid. The user expresses understanding after clarification and considers reworking the problem for better insight. The importance of correctly applying Kirchhoff's laws in circuit analysis is highlighted.
Ithryndil
142
0

Homework Statement


Determine the current in each branch of the circuit where R = 14.00 Ω, and V = 20.0 V.

attachment.php?attachmentid=15766&d=1223265869.jpg


(a) branch containing resistor R

(b) branch containing the 4.00 V source

(c) branch containing the voltage source V


Homework Equations



N/A

I have already completed the problem, but I want a bit of an explanation why things are they way they are in regards to the equations below:

I1+I2+I3 = 0
V1 - 6I1 - 14I3 = 0 (Left loop)
6I1 - 4I2 - V1 + V2 (Right loop)

Thanks for your help. I understand the one about the left loop, it's the right loop equation I am a bit hung up on.
 

Attachments

  • Circuit.JPG
    Circuit.JPG
    7.2 KB · Views: 757
Physics news on Phys.org
Ithryndil said:
6I1 - 4I2 - V1 + V2 (Right loop)

it's the right loop equation I am a bit hung up on.

Hi Ithryndil! :smile:

I assume it's the + or - sign for the Is that are worrying you?

The way you draw the arrows for the three currents is entirely arbitrary.

Of course, it's nice to make an intelligent guess as to which way the current will flow, so that all the Is come out positive.

But it doesn't matter in the slightest if you guess wrong, and put one of the arrows the wrong way round …

suppose you had labelled the arrow on I2 the other way …

you'd then get 6I1 + 4I2 - V1 + V2 (and of course I1 = I2 + I3 instead of I1 + I2 = I3), and your I2 would come out negative. :wink:

Does that help? :smile:
 
Yeah, I believe so. It's getting the signs the summation of it that had me, but after some further thought, I think I have it. I should probably redo the problem differently and see what I get.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top