Finding Resistors Currents with Changing Resistance

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A 23 V battery is connected to terminals A and B below.

(a) If R = 95 Ω, find the current in each resistor (/12, /55, /95).
(b) Suppose the value of R is increased. For the 12 Ω resistor, does the current flowing through it increase or decrease? What about the 55 Ω resistor? What about the 95 Ω resistor?

What I did for the /12 resistor is I = V/R = 23 V / 12 Ω = 1.9167, but got it wrong. Is this problem not as simple as I originally thought it is?

 

[stunner5000pt]

since the 12 ohm resistor and the 2 resistors in parallel are in series, the potential difference across the 12 ohm and the 2 parallel resistors is not the same so you can't simply do V= iR where V = 23 for the 12 volt resistor

you're going to have to find equivalent resistances for hte parallel ones first and then proceed

for b - would it make a difference?? Why?

 

[FlipStyle1308]

How do I find equivalent resistances? Do I solve I = 23/35 + 23/95 = 0.8992?

 

[stunner5000pt]

How do I find equivalent resistances?

your textbook should show how to combine 2 resistors whether they may be in series or parallel

in any case
for resistors in series; Req = R1+ R2+...

for resistors in parallel: $$\frac{1}{R_{eq}}= \frac{1}{R_{1}} + \frac{1}{R_{2}} + ...$$

 

[FlipStyle1308]

So is I = 23/35 + 23/95 = 0.8992? correct, in regards to the parallel resistors?

 

[stunner5000pt]

So is I = 23/35 + 23/95 = 0.8992? correct, in regards to the parallel resistors?

how did you arrive at that??
sorry I am too lazy to do it myself

 

[FlipStyle1308]

I already showed my work in that. I = V/R1 + V/R2 = 23/35 + 23/95 = 0.8992

 

[stunner5000pt]

I already showed my work in that. I = V/R1 + V/R2 = 23/35 + 23/95 = 0.8992

no

wheres the 35 coming from?? I ll assume you meant tosay 55...

when two resistors are in series (the 12 and the 55/95 parllel) is the potential diffrerence across the 12 and the 55/95 the same? Note that the 55/95 are in series, the current may be the same, but the potential difference is NOT. Although if the 12 ohm resistor was not present you would be right but here the 12 ohm resistor makes thing s a little morei nteresting

try the equivalent resistor route.

 

[FlipStyle1308]

I'm sorry, you lost me there. Would you be able to help set up the equation for me?

 

[stunner5000pt]

I'm sorry, you lost me there. Would you be able to help set up the equation for me?

find theq equivlanet resistance of ALL the resistors first

 

[FlipStyle1308]

Okay, 1/Req = 1/R1 + 1/R2 + 1/R3 = 0.11204 Ω.

I don't know if this is moving in the right direction, but I also did:

(0.11204 Ω)^-1 = 8.9253 Ω.
I = E/Req = 23 V / 8.9253 Ω = 2.57695 A.

I hope this helped speed things up a bit.

 

[stunner5000pt]

Okay, 1/Req = 1/R1 + 1/R2 + 1/R3 = 0.11204 Ω.

I don't know if this is moving in the right direction, but I also did:

(0.11204 Ω)^-1 = 8.9253 Ω.
I = E/Req = 23 V / 8.9253 Ω = 2.57695 A.

I hope this helped speed things up a bit.

is 12 in parallel with the 55 and 95??

also when you complete the sum you have to invert your answer to get Req otherwise you have 1/Req

 

[FlipStyle1308]

12 is not in parallel with 55 and 95, so does this mean I don't include it when solving 1/Req?

 

[stunner5000pt]

12 is not in parallel with 55 and 95, so does this mean I don't include it when solving 1/Req?

yes
thts correct

 

[FlipStyle1308]

So Req = 1/55 + 1/95 = 0.0287 Ω^-1 = 34.833 Ω. Do I simply add 12 to this number?

 

[stunner5000pt]

So Req = 1/55 + 1/95 = 0.0287 Ω^-1 = 34.833 Ω. Do I simply add 12 to this number?

yes that is the total equivlaent resistnace

now you can find the current through that resistor


now since the 12 and the 34 are in series what can you say about the current passing through each? Also can you find the potential diffrence across each?

after that you know the current passing through the 12 and the 34. Since the 34 is 2 resisotrs(55/95) in parallel what is equal between them?? Can you find the current across each using that thing which is equal??

dont try to rush it... take it slow

 

[FlipStyle1308]

Eek...I still do not understand what you are asking. I looked through the book and lecture notes, and could not find anything that seemed relevant to help me answer your questions :(.

 

[stunner5000pt]

Eek...I still do not understand what you are asking. I looked through the book and lecture notes, and could not find anything that seemed relevant to help me answer your questions :(.

do them step by step

first
find the current through that resistor (the 12 + 38) which you just found

and then follow those steps only once you have completed each

when resistors are in parallel th potential diff across them is same but the current is not
total current = sum of the current across each

when resistors are in series the potential difference is not the same but the current is the same
total potential difference = sum of potentei8al diff across each

 

[FlipStyle1308]

Okay, so I = E/Req = 0.4911 A. Mathematically, what is the next step? I understand what you are saying with the resistors being in parallel and in series, but I do not know how to mathematically use that information.

 

[stunner5000pt]

Okay, so I = E/Req = 0.4911 A. Mathematically, what is the next step? I understand what you are saying with the resistors being in parallel and in series, but I do not know how to mathematically use that information.

dont go to the next step without completing each step

ok so this means taht the current across the 2 resistors in series (the 12 and 38) have the same current passing through because they are in series

now we know that the total current passing thru the 55 and 95 is 0.4911 but that doesn't help us becase the current passing thru each is different

so find the voltage across the 12 and the 38

now since resistors are in parallel have the sam potenetial difference across them the potential across the 38 is the smae as taht across the 55 and the 95

now u can find the current across each resistor

 

[FlipStyle1308]

Where is the 38 coming from?

 

[stunner5000pt]

Where is the 38 coming from?

sorry i emant 34 - the equivalent resistnace of the 55/95 in parallel

 

[FlipStyle1308]

I also don't know how to find the current using what I already know. I just looked through the book and found nothing. Can you tell me what equations to use?

 

[stunner5000pt]

I also don't know how to find the current using what I already know. I just looked through the book and found nothing. Can you tell me what equations to use?

can youfind the current across the 46 ohm reisistor??

this resistor you found by first combining 55/95 into 34 and them adding 12 ohms.

 

[FlipStyle1308]

The current across the 46 ohm resistor is 0.4911 A, which I found earlier.

 

[FlipStyle1308]

Is anyone able to help me complete this problem? I still haven't found an answer for either part yet.

 

[Astronuc]

V = IR => 23 V = I*(12+34.83 ohms) => I = 0.4911 A.

The voltage drop across a resistor is simply the current * resistance, and in this case the voltage drop across a 12 ohm resistor is (0.4911A)*(12 ohms).

Now the voltage across parallel resistors is the same, so each receives a portion of the current coming into or leaving the common node. It is apportioned according to the resistance, I = V/R.

The voltage across the parallel resistors 23 V - the voltage drop across the 12 ohm resistor.

For part b, one needs to understand R_eq as a function of R. So write a forumula for R_eq (R), and determines its behavior as R increases.

 

[FlipStyle1308]

Thank you so much for helping me through that confusing part (a). As for part (b), would the 12 ohm resistor decrease, the 55 ohm resistor increase, and resistor R increase?

 

[Astronuc]

Thank you so much for helping me through that confusing part (a). As for part (b), would the 12 ohm resistor decrease, the 55 ohm resistor increase, and resistor R increase?

The 12 ohm resistor is fixed and not changing.

As stunner mentioned, when resistors are parallel, they produce a different equivalent resistance.

1/R_eq = 1/R₁ + 1/R₂ + . . . + 1/R_N, for N resistors in parallel.

In the OP, 55 ohm is parallels with R, and in part a, R = 95 ohm.

Now part b asks what if R increases. So going back to R_eq ,

1/R_eq = 1/(55 ohm) + 1/R

and the resisance between A and B is 12 ohm + R_eq.

So what happens to R_eq when R increases?

What happens when R = 55 ohms, which is the same resistance as the other parallel resistance?

If the total resistance increases, the current has to decrease, by virtue of I = V/R.

 

[FlipStyle1308]

My options are only either increase or decrease for each, so remaining the same is not an option. What I did was plug in a 97 ohm for R instead of 05 ohm to get my answers of: 12 ohm resistor decrease, the 55 ohm resistor increase, and resistor R increase, and I just want to make sure this matches what you get.

But to answer your question, when R increases Req also increases.

 

[FlipStyle1308]

Bump! Is anyone able to determine if I am correct or not? Thanks.

 

[FlipStyle1308]

Hmm..I change my answer, so that when R increases, Req decreases. As for the other two...I say that the 12 ohm resistor would increase, and the 55 ohm resistor would decrease, is this correct?

 

[FlipStyle1308]

Is anybody able to help me complete this problem? I would like to finish this possibly today. Thanks.