Determine currents of a circuit

[jwxie]

Homework Statement

For the circuit in the figure, determine i₁to i₅

http://i55.tinypic.com/dokoc5.png

Homework Equations

current division: i_n = (R_equivalence / R_n) * i_total
R_{equivalence in parallel} = R1*R2 / R1+R2

The Attempt at a Solution

|| (parallel), and +s (series)

1ohms || 2ohms = R_eq1
R_eq1 || 4ohms = R_eq2
R_eq2 +s 3ohms

However, note that current i_3,4,5 are present. Parallel elements do not share the same current. I have trouble applying the current division.

If I assume I am only taking i3, i4, and i5, and let i₃ be the total current at that particular region, then the R_eqv is (2*1)/2+1 meaning 2/3
Then which R_n should I take?

The formula for current division is mentioned above.

Please let me how to solve this problem that involves multiple currents going around.

Thank you.

 

[jwxie]

actually problem solved.;
i figure that in the end i get a series.
from that series i can find i1, and because the rest are in parallel, i have the same voltage, which is found through the Req3 and i1.

But if you have anything else to say please do. Thank you!

 

[vk6kro]

I think you have it OK.

Work out the result of the 3 parallel resistors, then work out the voltage division between this resistor and the 3 ohms. To do this, you work out the total resistance and find the total current in this from 40 volts. Then IR to get the voltage across the bottom resistors.

Then you know the voltage across all the bottom resistors (because they are in parallel) so you can work out the currents in each of them.

Did you get an answer?

 

[jwxie]

@ vk6kro
Yes I did. Thank you for the comment though!

 

[DeeNos]

I would approach this problem by first drawing a simplified version of the circuit, with all the parallel elements combined and the series elements in a single line. This will make it easier to apply the current division formula.

Next, I would assign a variable to each of the currents in the circuit, such as i1, i2, i3, i4, and i5. Then, I would use the current division formula to calculate the value of each current.

For example, to find i1, I would use the formula in = (Requivalence / Rn) * itotal, where Requivalence is the equivalent resistance of the parallel elements, and Rn is the resistance of the element that i1 is passing through. In this case, Requivalence would be (1*2)/(1+2) = 2/3, and Rn would be 3ohms. So, i1 = (2/3)/(3) * itotal.

Similarly, I would use the current division formula to find the values of i2, i3, i4, and i5. Once I have all the values, I can use Kirchhoff's current law to check if the sum of all the currents at any point in the circuit is equal to the total current entering that point.

Overall, the key is to simplify the circuit and use the current division formula to calculate the values of each individual current.