How Do You Simplify an ADC Circuit Using Kirchhoff's Laws?

[Selwin]

Hello,

I do not know if it's really upper physics but I have some exercices to do and I find them a bit difficult for a beginning.

This is a circuit: http://up.sur-la-toile.com/iu7M

I'm asked to simplify it like shown on the drawing so that afterwards I get this circuit: http://up.sur-la-toile.com/iu7L

I can simplify it by following the instance but I just would like to know what formula was used to simplify the circuit.

2) Then I have to determine the relation between r and R; Va7, E and R then I'm supposed to deduce I7. This is what I've done (using Kirchhoff's laws):

I7=Va7/2(R+r) is it correct ? However, I don't see the relation between r and R except maybe: E=(R+r)i...

Thank you for any valuable help!

 

[gabbagabbahey]

Hello,

I do not know if it's really upper physics but I have some exercices to do and I find them a bit difficult for a beginning.

Hi Selwin, welcome to PF!

This type of problem should probably be posted in the introductory section in the future.

I can simplify it by following the instance but I just would like to know what formula was used to simplify the circuit.

When going from (a) to (b), you simply use the formula for two resistors in parallel. When going from (b) to (c), you use the formula for two resistors in series...do you see why?

2) Then I have to determine the relation between r and R; Va7, E and R then I'm supposed to deduce I7. This is what I've done (using Kirchhoff's laws):

I7=Va7/2(R+r) is it correct ?

Close, the EMF/voltage in the circuit is E-Va7. (E pushes the charges clockwise and Va7 pushes the counter-clockwise)

However, I don't see the relation between r and R except maybe: E=(R+r)i...

If you apply the method in the first diagram 7 more times, you should be able to easily express $r$ in terms of $R$.

 

[Selwin]

Hello,

Sorry for my "short" silence and thank you for your reply gabbagabbahey.

I had the time to read what you've written and think about the solution thouroughly.

When going from (a) to (b), you simply use the formula for two resistors in parallel. When going from (b) to (c), you use the formula for two resistors in series...do you see why?

I think I do.

By the way, the teacher gave us the correction sooner as planned so...Still thank you, it helped me very much to better understand the correction then =)

See all of you ^^ (soon ?!)