What is the current in Resistor2?

[DuckAmuck]

Diagram1: http://i.imgur.com/StJae.png
Diagram2: Close the switch http://i.imgur.com/PnSIH.png
What is the current in resistor2? Please show the math. Thank you. [No, it's not a homework problem, I'm just curious.]

Some people say it would short out on resistor 2 and current would be zero, but that's supposedly not right. The current becomes some fraction of what it would be if R2 were in series with R1.

I am aware of Kirchoff's laws, but this is still stumping me. Thanks in advance.

 

[Doc Al]

Some people say it would short out on resistor 2 and current would be zero, but that's supposedly not right.

What do you say?

The current becomes some fraction of what it would be if R2 were in series with R1.

What fraction?

Once the switch is closed, is there a difference between your two diagrams?

 

[DuckAmuck]

No, no difference.

 

[Doc Al]

No, no difference.

OK, so what's the equivalent resistance of R2 and the bare wire, which are in parallel?

When current flows through that combination, what percentage would go through the wire?

 

[DuckAmuck]

That's exactly what I don't know.

 

[Doc Al]

That's exactly what I don't know.

Well, start there. What's the equivalent resistance of two resistors in parallel?

 

[DuckAmuck]

Rp = (1/R2 + 1/W)^(-1)
where W is the resistance of the wire.

 

[Doc Al]

Rp = (1/R2 + 1/W)^(-1)
where W is the resistance of the wire.

Good. So what will you put as the resistance of the wire?

 

[Captain Slog]

The problem here is between the abstract theoretical perfect components in a circuit diagram, and the reality of a practical component. Your piece of wire across R2 and your closed switch both have a theoretical resistance of zero ohms. Of course, in practice there would be some small resistance in both. If you want the 'real' and accurate figure for the current you will need to know these values. You may also find that the values change with time as the current heats the wire and the switch. You would need details of this dynamic too for a realistic calculation. Further more, the cell has an internal reactance, and the whoe circuit has inductance and capacitance. This will play a part during the transient when the switch is closed. But we are talking about very small quantities here - to all intents and purposes the switch shorts out R2 and the current through R2 is zero.

 

[Doc Al]

The problem here is between the abstract theoretical perfect components in a circuit diagram, and the reality of a practical component.

I highly doubt that that is the issue here.

 

[Captain Slog]

Ha ha - I think you might be right. I stand corrected.