How to Apply Kirchoff's Laws to Solve Resistive Circuit Problems

In summary, Kirchoff's Loop/Junction Rule states that the voltage drop across two resistors in a circuit is the same. This was used to find the current through the third resistor, R3, which was 5A.
  • #1
Yosty22
185
4

Homework Statement



In the following figure(Figure 1) the battery has emf 26.0V and negligible internal resistance. R1 = 4.10Ω . The current through R1 is 1.50A and the current through R3 = 5.00A
What are the resistances of R2 and R3?
(Image Attached)

Homework Equations



Kirchoff's Loop/Junction Rule

The Attempt at a Solution



I am having some real problems with Kirchoff's Rules. Can someone help me figure out how to begin? I started out by saying that Since the current through R3 is 5A, then that is the same as the current that gets split at the junction into I_1 through R_1 and I_2 through R_2. Also, I know that the voltage drop across R_1 is equal to the voltage drop across R_2 which is 6.15V. Using this, I said that (R_2)(I_2)=6.15V. I was given I_1 (the current through R_1) and I believe the current that enters the junction is the 5A that were given in the problem that go through R_3. Using that, I said that I_2 + I_1 = 5A. Knowing I_1, I found that I_2 should be .9A, which would make R2=6.833 Ohms. I don't know if this is right. Even if it is, how do I go about solving for R_3? I am very confused. Any help would be great.
 

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  • #3
Yosty22 said:
... I was given I_1 (the current through R_1) and I believe the current that enters the junction is the 5A that were given in the problem that go through R_3. Using that, I said that I_2 + I_1 = 5A. Knowing I_1, I found that I_2 should be .9A,

Uh ... you might want to take a remedial course in arithmetic here :smile:

I mean, .9 + 1.5 = 5.0 ?
 
  • #4
Oh woops, I didn't see that. So in that case, I_2 = 3.5A, not 0.9. so the voltage drop across R_2 is the same as that across R_1, which I know is 6.15V. Therefore (3.5A)(R_2)=6.15V. Is this correct?
 
  • #5
Yeah that seems right. You got that from the loop thru the battery right?

i1*r1 + i3*r3 - 26 = 0 with i1*r1 = (1.5)(4.1) = 6.15 V and since you know i2=3.5A ...

ALso you should still read the wiki article as it mentions the restrictions on K's laws for AC circuits and when magnetic fields are present.
 
  • #6
Ok, thank you. So that would make R_2 = 1.757 Ohms. So how would I go about finding R_3? I already know the current through there, but what do I do about the EMF? Should I find the equivalent resistance of the top loop, then write another equation using Kirchoff's Law around the whole outer loop? So find R_eq for R_1 and R_2, then have I(R_eq)+I_3R_3-EMF=0? However, if I find R_eq, would the voltage drop be the same as each individual one, allowing me to solve for the current that would flow through R_eq?
 
  • #7
whats the voltage drop across R3? you were able to determine the voltage drop across R1 and R2.
 
  • #8
That is what I am unsure how to find. Would I have to find the equivalent resistance for R1 and R2 and then write another equation since I know the current through R3 already?
 
  • #9
Yosty22 said:
That is what I am unsure how to find. Would I have to find the equivalent resistance for R1 and R2 and then write another equation since I know the current through R3 already?

Doesn't the problem say the voltage source is 26V and you know its 6.16V across the R1/R2 piece so now what is it across the R3?
 
  • #10
Is it just 26-6.16?
 
  • #11
Yosty22 said:
Is it just 26-6.16?

Good question. Is it ?
 
  • #12
Im pretty sure it is, but I cannot think of why that would be. Any insight?
 
  • #13
Yosty22 said:
Im pretty sure it is, but I cannot think of why that would be. Any insight?

Look at K voltage law again, what does it say about summing voltages in a loop?
 
  • #14
Ahh, so the emf + the voltage on each resistor has to add up to 0. Then once I solve for the voltage of R3, I know the current, so I can find the resistance. Is that correct in my thinking?
 
  • #15
Yosty22 said:
Ahh, so the emf + the voltage on each resistor has to add up to 0. Then once I solve for the voltage of R3, I know the current, so I can find the resistance. Is that correct in my thinking?

Yes.
 
  • #16
Thank you very much for all of your help. I was having a lot of trouble visualizing this and the steps you have to break things down into. I really appreciate all of your help and putting up with what seems to be nothing short of my ignorance on how to approach this. I really appreciate it.
 

1. What is Kirchoff's Law Problem?

Kirchoff's Law Problem refers to a set of fundamental laws in physics that describe the behavior of electrical circuits. These laws were developed by Gustav Kirchoff in the mid-19th century and are widely used in the analysis and design of electrical circuits.

2. What are the two laws in Kirchoff's Law Problem?

The two laws in Kirchoff's Law Problem are Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL). KCL states that the sum of currents entering a node in an electrical circuit must equal the sum of currents leaving that node. KVL states that the sum of voltage drops around a closed loop in a circuit must equal the sum of voltage sources in that loop.

3. Why are Kirchoff's Laws important in electrical circuits?

Kirchoff's Laws are important in electrical circuits because they allow us to analyze and solve complex circuits by using basic principles. They also help us understand the flow of current and voltage in a circuit, making it easier to design and troubleshoot circuits.

4. How do you apply Kirchoff's Laws in a circuit?

To apply Kirchoff's Laws in a circuit, you first need to identify all the nodes and loops in the circuit. Then, use KCL to write equations for each node and KVL to write equations for each loop. Finally, solve the resulting system of equations to determine the unknown currents and voltages in the circuit.

5. Can Kirchoff's Laws be applied to any type of circuit?

Yes, Kirchoff's Laws can be applied to any type of circuit, whether it is a simple series or parallel circuit, or a more complex network of circuits. As long as the circuit follows the basic principles of electricity, Kirchoff's Laws can be used to analyze and solve it.

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