Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

inkyvoyd

  • one year ago

Branch current analysis (Part 3 where I get scared)

  • This Question is Closed
  1. inkyvoyd
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In previous notes, I have introduced Ohm's law, and its generalizations KVL and KCL. I will now show you a simple example where parallel-series analysis will not apply. Example problem 1.

  2. inkyvoyd
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Determine the currents in i_1, i_2, and i_3. Remember to do this with reference to the direction indicated by the arrows. It should be quite evident that the resistors are not connected in parallel or series - there are two power sources. We shall apply Kirchoff's laws to determine the answer regardless. There are a number of ways to do this, but a straightfoward way uses KCL, KVL, and Ohm's law- you'll find that you can formulate systems of equations with regards to the current of the junctions. Note that although you might not know the current's themselves, you can express them using Ohm's law, I=V/R. Step 1: Choose a reference node to start the problem from. Let's use node 1. Step 2: Label the current paths to and from this reference node (I_1,I_2,I_3)

  3. inkyvoyd
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Step 3: Formulate your first equation using KCL. In this case it would be: I_1-I_2+I_3=0 Step 4: Formulate subsequent equations using KVL around closed loops. The twist to this is that we use Ohm's law to express the unknown voltage drops across resistors (remember that R1_v=6*I_1). Thus we have on the left side -12+6*I_1+4*I_2=0, because -B1_v+R1_r*I_1+R2_r*I_2=0 We also have 6-4*I_2-2*I_3=0 We then have a system of 3 equations in 3 variables. I_1-I_2+I_3=0 -6-4*I_2-2*I_3=0 -12+6*I_1+4*I_2=0 Solving for this yields I_1=24/11 I_2=-3/11 I_3=-27/11 The negative sign means that the current is flowing in the direction opposite to the arrow indicated. Thus, we have calculated the currents flowing in and out of Node 1. Further application of Ohm's law allows one to obtain values for voltage drops and currents.

  4. inkyvoyd
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    UPDATE: I have added 6 more examples.

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.