🧵 Resistances in a parallel branch
Anonymous at Sat, 9 Nov 2024 11:49:53 UTC No. 16468174
I've got a physics question: let's say I have a circuit with two resistors connected in parallel. The fixed resistor and variable resistor both have a non-zero value of resistance.
If I decrease the resistance of the variable resistor, the overall resistance of the circuit decreases. But what happens when the variable resistor's resistance goes down to zero? Will the circuit effectively become a series circuit, causing the resistance to go back up? Or will the overall resistance just tend to zero forever? Or something else entirely?
Pic related is the circuit
Any help would be appreciated
Anonymous at Sat, 9 Nov 2024 12:27:07 UTC No. 16468218
why should it go back up? the resistance will be 0 and the remaining short circuited resistor will be obsolete.
Anonymous at Sat, 9 Nov 2024 12:48:43 UTC No. 16468232
>>16468174
Just use linear algebra
Anonymous at Sat, 9 Nov 2024 12:57:21 UTC No. 16468235
>>16468174
Thevenin equivalents don't work with short circuits or open circuits. What you'll have as the variable resistance goes to zero is a short.
Anonymous at Sat, 9 Nov 2024 13:08:58 UTC No. 16468242
>>16468174
Resistors in parallel with a small resistor are roughly equivalent to the small resistance because current flows mostly through the small resistance branch.
Resistors in series with a big resistor behave roughly like the big resistor because current has to flow through all of the resistors and the big one has the most effect.
In your case if you give one of the branches no resistance at all then the resistance across the parallel branches is roughly zero because all of the current will flow through the path with no resistance and none of it ever sees the resistor in the other branch (i.e. you've short circuited it).
Anonymous at Sun, 10 Nov 2024 06:20:37 UTC No. 16469314
>>16468218
>>16468232
>>16468235
>>16468242
Do any of you actually understand or are you just saying random words to try sound smart
Anonymous at Sun, 10 Nov 2024 06:24:20 UTC No. 16469317
>>16468218
This poster is correct.
Anonymous at Sun, 10 Nov 2024 16:05:11 UTC No. 16469701
>>16469314
Using linear algebra to analyze circuits is literally taught to you in high school. If you don't didn't pay attention in school then why should anyone hold your hand now?
Anonymous at Sun, 10 Nov 2024 22:00:07 UTC No. 16470023
>>16469314
I'm an EE working on a PhD. I've literally taught intro to circuits classes. You're getting got by missing a simple divide by zero issue in simple algebra.
Anonymous at Mon, 11 Nov 2024 15:31:10 UTC No. 16470853
>>16468174
Overall resistance (R) should be like that :
1/R = 1/r1 + 1/r2 + ...
You're variable resistance in your pic is 1/r2 :
If r2 goes to a higher magnitude than r1, then 1/r1 >>> 1/r2, and (1/r1 + 1/r2) ~ 1/r1
If r1 and r2 are in the same magnitude order, R = (r1+r2)/(r1*r2)
(intuitively you can see that the overall R decrease rapidly the more you add r in parallel in the circuit).
If r2 decrease to 0, then you have (1/r1 + "infinity"), then R ~ 0 = short circuit
This guy is correct :
>>16468218
This guy says shit :
>>16468235
Thevenin equivalence totally works with the 2 extreme possibilities.
Anonymous at Mon, 11 Nov 2024 16:12:28 UTC No. 16470904
>>16470853
I'm sorry, what exactly is (1/R_1+1/R_2)^(-1) when R_1 is zero.
You're talking shit mate. The equivalent resistance formula only works when both resistances are non-zero.
Thevenin equivalents "work" for R^infty only if there is still a closed circuit after the R^infty case. If there is no closed circuit after your asymptotics, it by definition doesn't work.
Anonymous at Mon, 11 Nov 2024 16:22:01 UTC No. 16470920
>>16470904
>(1/R_1+1/R_2)^(-1) when R_1 is zero.
1/r1 = 1/0 = "infinity"
"infinity" + 1/r2 ~ "infinity"
1/R = "infinity"
R = 0 = short-circuit
Simple math.
>If there is no closed circuit after your asymptotics, it by definition doesn't work.
Ok, my bad.
Physically, the circuit is short, so "boom".
Mathematically, it's just a special case in Thevenin's equivalence, no big deal.
Anonymous at Mon, 11 Nov 2024 16:50:02 UTC No. 16470965
>>16470920
Mathematically, maybe? It's hard to say where the line is when you're talking about highly idealized concepts like "linear resistance" anyways.
They are just kind of heuristics we use to simplify things into ODE's/linear algebra a which is close enough. Physically, Rth being zero means you have a house fire where your circuit board used to be, and Rth to infinity means you don't have a circuit at all anymore.
Anonymous at Mon, 11 Nov 2024 17:05:55 UTC No. 16471006
Equivalent resistance for parallel resistors is R1*R2/(R1+R2). If one of the resistances goes to zero clearly the equivalent resistance goes to zero.
Anonymous at Mon, 11 Nov 2024 18:32:30 UTC No. 16471110
>>16468174
Thevenin is nt needed if you just look at the physics involved.
If the variable resistor goes to zero, it essentially short circuits the entire circuit, and the value of the fized resistor is irrelevant.