Question on Kirchoff's Laws

[ahben86]

I was hoping someone could help out, I am working out a problem with Kirchoff's Laws and cannot seem to get the math to work out properly, at least I think the math is not working properly.
I was hoping to run it by someone here.

Homework Statement

The circuit is as follows:
A battery of 24 V on one end connected to two parallel resistors with values of 5 Ω and 7 Ω.
Mesh one will be the loop between the battery and the 5 Ω resistor, which has a current of I₁.
Mesh two will be the loop between the 5 Ω resistor and the 7 Ω resistor, which has current of I₂.

Homework Equations

The equations I set up are as follows:
0 = -24 + 5*(I₁ - I₂)
0 = 7*I₂ + 5*(I₂ - I₁)

The Attempt at a Solution

After calculating the values I obtained these numbers:
I₁ = 8.229 A
I₂ = 3.429 A

I tried verifying these answers by using V = I*R
Finding R_eq to be 2.917 Ω.
Therefore I = V/R and I = 8.228 A and since the current from I₁ is the same value it seems that the values obtained from Kirchoff's Laws do not match the Ohm's Law current.

I am uncertain if I am not realizing a concept but this does not make sense to me.

Any help is appreciated.
Thank you,
A.B.

 

[Delphi51]

I think your work is all correct. V =IR finds the current through the resistors as 4.8 and 3.42 representing I1 - I2 and I2, so I2 = 3.42,
I1 - I2 = 4.8
I1 = I2 + 4.8
I1 = 3.42 + 4.8 = 8.23

 

[ahben86]

thank you for your help Delphi, sorry I posted in the wrong area.
I think I understand now,

A. B.

 

[Delphi51]

Most welcome! This is the correct area for your question.

 

[asteriatic]

Hello A.B.,

Thank you for reaching out for help with your problem involving Kirchoff's Laws. It seems like you have set up the equations correctly, but there may be a mistake in your calculations. I would suggest double checking your math to ensure accuracy. Additionally, it may be helpful to draw out the circuit and label all the components and currents to visualize the problem better.

In terms of verifying your answers using Ohm's Law, it is important to note that the currents calculated using Kirchoff's Laws are the total currents in each loop, whereas the current calculated using Ohm's Law is the current through a single resistor. This is why the values may not match exactly. However, the total current through the entire circuit should still be equal to the total current calculated using Ohm's Law.

I hope this helps. If you are still having trouble, don't hesitate to reach out for further assistance. Good luck with your problem!

Best,