Finding the Current in a Resistor in a Closed Circuit

AI Thread Summary
The discussion focuses on calculating the current in resistor 2 of a closed circuit with an ideal battery of 7.7 V. The user successfully determined the resistance values for resistors 1, 2, and 3 using the given voltage and current scales. They calculated the equivalent resistance and found the overall current to be approximately 0.001761 A. Two methods are suggested for finding the current in resistor 2: using the current ratios based on resistance values in parallel or calculating the voltage drop across resistor 3. Both methods provide a pathway to solve for the current in the circuit effectively.
MedEx
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1. Homework Statement
The ideal battery in Figure (a) has emf
img1336925519406_1870594626818166.gif
= 7.7 V. Plot 1 in Figure (b) gives the electric potential difference V that can appear across resistor 1 of the circuit versus the current i in that resistor. The scale of the V axis is set by Vs = 18.9 V, and the scale of the i axis is set by is = 3.17 mA. Plots 2 and 3 are similar plots for resistors 2 and 3, respectively. What is the current in resistor 2?

Homework Equations


Req for resistors in parallel is 1/Req = 1/R1 + 1/R2 +1/R3...
Req for resistors in series is Req = R1 + R2 + R3...
V=iR
Resistors in parallel have same V, resistors in series have same i

The Attempt at a Solution


I found R1 to be 5962.15 through Vs/is
I found R2 as 2/3 Vs/is or 3974.76
R3 as 1/3 Vs/is or 1987.38
Req = R3 + 1/(1/R2+1/R1) or 4372.24 ohms
Then using V=iR (7.7V=4372.24i) I found to be .001761A

If every resistor had the same current/voltage I feel like I could do it but I'm not sure how to put things in terms of each other.
 
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Could you provide figures (a) and (b)?
 
MedEx said:
Sorry about that. The figures show up on my screen but never on anyone else's i guess
Use the UPLOAD button in the lower right of the Edit window to attach figures to your posts... :smile:
 
MedEx said:
I found R1 to be 5962.15 through Vs/is
I found R2 as 2/3 Vs/is or 3974.76
R3 as 1/3 Vs/is or 1987.38

OK, I agree with your reasoning. So now you know the value of each resistor. And your calculation of the overall current appears to be correct as well.

Two ways to proceed here.
Method 1:
MedEx said:
Resistors in parallel have same V,
Because of that, I = V/R in the branches of the parallel portion, is inversely proportional to R. You know the ratio of R1 and R2, so that tells you the ratio of the currents through them. And you know those two currents have to add up to the total current flowing through the circuit. That's enough to solve for the current through each one.

Method 2:
This one might be easier to understand. The voltage drop across R3 is V = I*R3. Knowing that tells you what the voltage across R2 is (which is also the voltage across R1 of course).
 
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