Current electricity and circuits

[Abhishekdas]

Current electricity...

Homework Statement

In the circuit shown(please refer to attchment) only thing missing is that the battery has an internal resistance of r. Now When key K1 is closed the ammeter reads I₀ whether K2 is open or closed. But when K1 is open the ammter reads I₀ /2 when K2 is closed. Assuming that ammeter resistance is much less than R2 find R1 and r.
Here R2=100 ohm and R3 = 100 ohm

Homework Equations

The Attempt at a Solution

Now in the diagram no Ammeter is visible ...So i proceeded assuming that ammeter is attached to the main circuit ie anywhere near the battery...Now i don't get this "When key K1 is closed the ammeter reads I₀ whether K2 is open or closed"...how can this I₀ be independent of R3?

 

[Abhishekdas]

Waiting for a reply soon...thank you...

 

[gneill]

At first glance, I don't see any place where an ammeter could be placed that would be unaffected by opening and closing K2 while K1 is closed.

When K1 is closed it short-circuits resistor R1. That effectively removes R1 from the circuit, since no potential difference can be developed across it. If you then redraw the circuit for this case (K1 closed), you have what I show in the attached image.

Now, where could you put an ammeter in that circuit such that its reading would be unaffected by K2? The internal resistance of the battery (what I've shown as Ri) will have different voltage drops depending upon whether K2 is open or closed. This will affect currents in all branches. (Perhaps this is telling you something about the value of the internal resistance).

 

[Abhishekdas]

Ya... i agree with you...So basically it seems there is something wrong with the question isn't it? I guess better off leaving it...Just wanted to confirm that my concepts are fine...

Thank you gneill...

 

[gneill]

Ya... i agree with you...So basically it seems there is something wrong with the question isn't it? I guess better off leaving it...Just wanted to confirm that my concepts are fine...

Thank you gneill...

Suppose that the ammeter were placed in series with R2, and further suppose that Ri and R1 were zero ohms. How would the circuit operation compare against their description?

 

[Abhishekdas]

This time...the current through current is independent of K2...right...
In the book the answer for internal resistance is as you say 0 but R1 is 50...
But R1 can't be non zero because in such a case the current in ammeter is not independent of k2...Isnt it? So R1 = 0 and Ri being 0 is the only case that makes sense...

 

[gneill]

That's what it looks like to me, given your initial drawing.