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

[Yosty22]

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.

 

[jedishrfu]

Read the wikipedia writeup and see if it helps:

http://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws

I noticed you said i1=1.5A and the total flow is 5A so the current thru R2 can't be 0.9A right?

 

[phinds]

... 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

I mean, .9 + 1.5 = 5.0 ?

 

[Yosty22]

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?

 

[jedishrfu]

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.

 

[Yosty22]

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?

 

[jedishrfu]

whats the voltage drop across R3? you were able to determine the voltage drop across R1 and R2.

 

[Yosty22]

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?

 

[jedishrfu]

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?

 

[Yosty22]

Is it just 26-6.16?

 

[phinds]

Is it just 26-6.16?

Good question. Is it ?

 

[Yosty22]

Im pretty sure it is, but I cannot think of why that would be. Any insight?

 

[jedishrfu]

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?

 

[Yosty22]

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?

 

[jedishrfu]

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.

 

[Yosty22]

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.