Art of Electronics question 1.4

[Richardcavell]

In The Art of Electronics, 3rd edition,

I have photographed the question. The next photo is my answer. I am satisfied that it works. But in the third photo, I am alluding to an idea. What I really want to do is what’s in the fourth photo.

[jwet]

I can think of a few ways to do it-

A hint- you can always take a subcircuit of parallel R's and make an equivalent single R.  If you take N-1 resistors and consolidate them into one R and then add the last- does this give you an idea?

[golden_labels]

A hint: conductance.

[Terry Bites]

Legit

[wasedadoc]

A hint: conductance.

Did you mean "induction"?

https://en.wikipedia.org/wiki/Mathematical_induction

[ebastler]

A hint: conductance.

Did you mean "induction"?

https://en.wikipedia.org/wiki/Mathematical_induction

No, I don't think that's what he meant. But you got the "Wikipedia" bit right. 
https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance

[wasedadoc]

A hint: conductance.

Did you mean "induction"?

https://en.wikipedia.org/wiki/Mathematical_induction

No, I don't think that's what he meant. But you got the "Wikipedia" bit right. 
https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance

The OP's question was about the fourth photo.  Conductance is at the heart of the first equation in that photo, but I could argue that going from that equation to the second one is mathematical induction.

[ebastler]

The OP's question was about the fourth photo.  Conductance is at the heart of the first equation in that photo, but I could argue that going from that equation to the second one is mathematical induction.

Well, once you phrase the problem in terms of conductance, you don't really need to bring out the heavy artillery to see that a+(b+c+d) = a+b+(c+d) = a+b+c+d. 

[golden_labels]

In the exercise we read “beginners tend to get carried away with complicated algebra […]. Now is the time to begin learning intuition and shortcuts.” I take that as a suggestion to not use algebraic approach. If one states the problem in terms of conductance, it becomes equivalent to joining small pipes to make a large one.



I believe this is something so intuitive, that a child would understand the concept.

[Smokey]

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