Determine currents of a circuit

In summary, for the circuit shown in the figure, the task is to determine the values of i1 to i5. The problem involves multiple currents and the use of current division and parallel and series resistors. By calculating the equivalent resistances and using voltage division, the values of i1 to i5 can be found. The commenter confirms that the problem has been solved and suggests a method to find the values.
  • #1
jwxie
281
0

Homework Statement



For the circuit in the figure, determine i1to i5

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


Homework Equations



current division: in = (Requivalence / Rn) * itotal
Requivalence in parallel = R1*R2 / R1+R2

The Attempt at a Solution



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

1ohms || 2ohms = Req1
Req1 || 4ohms = Req2
Req2 +s 3ohms

However, note that current i3,4,5 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 Reqv is (2*1)/2+1 meaning 2/3
Then which Rn 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.
 
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  • #2
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!
 
  • #3
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?
 
  • #4
@ vk6kro
Yes I did. Thank you for the comment though!
 
  • #5


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.
 

Related to Determine currents of a circuit

1. What is the purpose of determining currents in a circuit?

Determining currents in a circuit is important for understanding how electricity is flowing through the various components of the circuit. This information can help troubleshoot any issues and optimize the performance of the circuit.

2. How do you calculate the current in a circuit?

To calculate the current in a circuit, you can use Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R). This can be represented by the formula I = V/R.

3. What factors affect the current in a circuit?

The current in a circuit can be affected by the voltage of the power source, the resistance of the circuit components, and the type of circuit (series or parallel). Changes in these factors can cause variations in the current flowing through the circuit.

4. Can you use a multimeter to determine currents in a circuit?

Yes, a multimeter can be used to measure the current in a circuit. Set the meter to the appropriate current range and connect it in series with the circuit. The meter will display the current flowing through the circuit.

5. How can you use the information about currents to improve a circuit's performance?

By determining the currents in a circuit, you can identify areas where there may be too much or too little current. This can help you optimize the circuit by adjusting component values or identifying any potential issues that may be affecting the current flow.

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