Simple Combination Circuit, Find Current

[blue_lilly]

Homework Statement

Combinations of Resistors

Im not sure if the image will show up. If the image doesn't show up; it is similar to this picture http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/sparal6.gif
In the link's picture R1 is in the correct spot, R2 is R6-5-4 and R3 is R3-2. Sorry if there is any confusion.

Given the circuit shown below, the power supply is set to a voltage V=18.3 V, R2 = 33.2 Ω, and R3 = 46.5 Ω. Suppose you place an ammeter into the circuit and find that the current through R2 is 0.263 A. Answer the following questions:

A)What is the voltage across resistor R2? 8.74 V This is correct
B)What is the current through resistor R3? 0.188 A This is correct
C)What is the current flowing through R1? 0.451 A This is correct

D)What is the resistance of resistor R1? I NEED HELP ON THIS ONE

Homework Equations

V2 = R2 * I2
I3 = V3 / R3
I1(series)= I2 + I3 (Parallel)
R1 = V1 / I1

The Attempt at a Solution

A) V2 = R2 * I2 = 33.2 *.263 = 8.74
Voltage going through resistor 2 is 8.74 V

B) I3 = V3 / R3 = 8.74/46.5 = .188 A
Current going through resistor 3 is .188 A

C) I1(series)=I2 + I3 (parallel) = I1 = .188 + .263= .451 A
Current going though resistor 1 is .451 A

D) THIS IS THE PART I NEED HELP WITH!
R1 = V1 / I1 = 18.3/.451 = 40.57 ohms

This answer is not correct and I am not sure why. I thought that the way to find resistance was R= V/I. I solved for the correct current in the previous problem and we are given that V= 18.3 V in the wording of the problem.

Any help would be greatly appreciated!

 

[gneill]

Your image is a bit hard to see, given that it's blue lines on a black background (for my viewer at least). So here I've rendered it as I understand it (note that you can upload gif files if you use the Advanced editing panel):

Note that your voltage V1 = 18.3 V is not across R₁ alone. Try writing KVL around a loop with R₁ in it.

 

[blue_lilly]

Your image is a bit hard to see, given that it's blue lines on a black background (for my viewer at least). So here I've rendered it as I understand it (note that you can upload gif files if you use the Advanced editing panel):

Note that your voltage V1 = 18.3 V is not across R₁ alone. Try writing KVL around a loop with R₁ in it.

So, the voltage that they gave is for the total circuit then?
If that's the case then I can subtract the V1(8.74) and V2(8.74) from it.
Vtot = V1 + V2 + V3
18.3 = V1 +8.74 + 8.76
V = .82 volts going though R1

Then would you take R1 = V1 / I1 = .82/.451 = 1.818 ohms ?

 

[gneill]

So, the voltage that they gave is for the total circuit then?
If that's the case then I can subtract the V1(8.74) and V2(8.74) from it.
Vtot = V1 + V2 + V3
18.3 = V1 +8.74 + 8.76
V = .82 volts going though R1

Then would you take R1 = V1 / I1 = .82/.451 = 1.818 ohms ?

No, that's not correct.

Okay, first, voltage does not go "through" a component. Voltage is across components. It's the potential difference from one end to the other. Second, the voltages across parallel components are the same voltage. You don't sum them! They are not in series.

So when I suggested that you write KVL for a loop including R1, you cannot have both R2 and R3 in that loop, you can only have one or the other. Try tracing a loop through the voltage source and R1...

 

[blue_lilly]

No, that's not correct.

Okay, first, voltage does not go "through" a component. Voltage is across components. It's the potential difference from one end to the other. Second, the voltages across parallel components are the same voltage. You don't sum them! They are not in series.

So when I suggested that you write KVL for a loop including R1, you cannot have both R2 and R3 in that loop, you can only have one or the other. Try tracing a loop through the voltage source and R1...

I think I get it. The current would only go down one of the parallel resistors so I shouldn't have subtracted the voltage lost across the resistors for both R2 and R3.
Vtot= V1 + V2
18.3 = V1 + 8.74
V1 = 9.56 Volts lost across R1

R1 = V1 / I1 = 9.56 / .451 =21.2 ohms

 

[gneill]

I think I get it. The current would only go down one of the parallel resistors so I shouldn't have subtracted the voltage lost across the resistors for both R2 and R3.
Vtot= V1 + V2
18.3 = V1 + 8.74
V1 = 9.56 Volts lost across R1

R1 = V1 / I1 = 9.56 / .451 =21.2 ohms

Huzzah! Yes, that looks good!

 

[blue_lilly]

Huzzah! Yes, that looks good!

All right, thanks so much for your help! I really appreciate it!