Finding the voltage of the circuit (resistor ladder)

[deskochan]

Homework Statement

Finding the voltage of the circuit (resistor ladder)

Relevant Equations

Resistor Ladder?

The answer is B.
My question:
(a) What is the basic approach to start to think about this problem: Equivalent resistance? ohm's law?
(b) What is the purpose of gamma = R2/(R1+R3) because I have no idea how it uses?
(c) Why the answer is an exponential drop of voltage?

 

[Delta2]

This reminisces me of transmission line theory. You basically have to choose an infinitesimal loop and use KCL and KVL to analyze it. If all go well you ll get one differential equation for Voltage $V(x)$ and one for the current $I(x)$

 

[deskochan]

This reminisces me of transmission line theory. You basically have to choose an infinitesimal loop and use KCL and KVL to analyze it. If all go well you ll get one differential equation for Voltage $V(x)$ and one for the current $I(x)$

I have only GCE A level physics background. How can I start to think about it? I do not expect to solve this question but at least how can I start to think from A level physics.

 

[BvU]

Hello @deskochan,

​

Picture is rather unsharp. Nice to know that b (not: B) is the answer, but

is illegible for me.

(a) What is the basic approach to start to think about this problem: Equivalent resistance? ohm's law?

That is rather obvious: they even give a hint ! What do you do with that hint ?

(b) What is the purpose of gamma = R1/(R1+R3) because I have no idea how it uses?

I don't see that definition. I do see $\gamma = {R_2/R_1+R_3}$. It comes back in the answer, so it seems to be useful. And it reduces the amount of writing needed.

(c) Why the answer is an exponential drop of voltage?

Because that is what comes out ?
Probably some infinite sum, but from the hint it can also be the solution of a differential equation ...

$\$

 

[Delta2]

I have only GCE A level physics background. How can I start to think about it?

Not sure how good can be a GCE A level physics background. Are you familiar with Kirchhoff's laws, Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL)?

 

[deskochan]

Hello @deskochan,

​

Picture is rather unsharp. Nice to know that b (not: B) is the answer, but View attachment 285911is illegible for me.That is rather obvious: they even give a hint ! What do you do with that hint ?I don't see that definition. I do see $\gamma = {R_2/R_1+R_3}$. It comes back in the answer, so it seems to be useful. And it reduces the amount of writing needed.Because that is what comes out ?
Probably some infinite sum, but from the hint it can also be the solution of a differential equation ...

$\$

Sorry for the poor resolution. it is -2x/(sqrt (4*gamma+1)+1).
What is the hint? Sorry for this question but I really have an interest.
Would you tell me more and I just have GCE A level physics and I think this question is out of A level.

 

[deskochan]

Not sure how good can be a GCE A level physics background. Are you familiar with Kirchhoff's laws, Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL)?

A little bit for self-study but not familiar because GCE A level seldom use it.

 

[Delta2]

Ok well, if you have not seen a treatment on transmission line theory, and you are not familiar with Kirchhoff's laws then probably this problem is beyond your level of knowledge. The differential equations I get by properly applying KVL and KCL are :
$$\frac{dV(x)}{dx}=-I(x)(R_1+R_3)$$
$$\frac{dI(x)}{dx}=-\frac{V(x)}{R_2}$$
But these have a bit different solution for $V(x)$ than the B) of the answer. I get $$V(x)=V_0e^{-\frac{x}{\sqrt{\gamma}}}$$

 

[deskochan]

Ok well, if you have not seen a treatment on transmission line theory, and you are not familiar with Kirchhoff's laws then probably this problem is beyond your level of knowledge. The differential equations I get by properly applying KVL and KCL are :
$$\frac{dV(x)}{dx}=-I(x)(R_1+R_3)$$
$$\frac{dI(x)}{dx}=-\frac{V(x)}{R_2}$$
But these have a bit different solution for $V(x)$ than the B) of the answer. I get $$V(x)=V_0e^{-\frac{x}{\sqrt{\gamma}}}$$

Yes, you are right. It is beyond my level. Thank you very much.

 

[BvU]

https://www.pravega.org/events/science_eve/decoherence/Decoherence_Prelims__Objective_.pdf

 

[deskochan]

https://www.pravega.org/events/science_eve/decoherence/Decoherence_Prelims__Objective_.pdf

View attachment 285914

Yep.