Single battery & Single resistor: Series or parallel?

[JJBladester]

Homework Statement

Can a circuit be both series and parallel? Not series-parallel, but series *and* parallel?

Let's say you have a battery with its positive terminal connected to a resistor and its negative terminal connected to the other end of the resistor.

Due to conservation of charge, the circuit is in series. Due to the resistor being connected directly across the battery, it has the same voltage as the battery and thus it is in parallel with the battery. Right?

So the circuit exists in both a series state and a parallel state...?

 

[nsaspook]

The battery has an internal resistance as does the resistor leads so the circuit is a serial resistance circuit. The voltage across the resistor will very close to the same voltage as the battery only as long as the value of the resistor is high compared to the other series resistance values.

 

[CWatters]

So the circuit exists in both a series state and a parallel state...?

Correct. A circuit can have components that are in series, parallel, both at the same time or neither. They are only ways to view a circuit (or parts of a circuit) to help analyse it.

 

[JJBladester]

Correct. A circuit can have components that are in series, parallel, both at the same time or neither. They are only ways to view a circuit (or parts of a circuit) to help analyse it.

This question has bugged me since I started my B.S. in EET. I was too afraid to ask it because it seemed "elementary". Thanks for the confidence boost. :)

 

[CWatters]

Just to add it's quite common to change your view of how a circuit is configured... For example in this circuit when the switch is made you might choose to analyse the R and C as being in parallel with each other and the battery. Then when the switch is opened it makes more sense to view the C and R as being in series with each other.

A general rule is that

Components in parallel have the same voltage across them.
Components in series have the samecurrent through them.

 

[nsaspook]

A general rule is that

Components in parallel have the same voltage across them.
Components in series have the same current through them.

I would look at the problem using Kirchoff's "Loop" Rule with a "real battery".
http://www.physics.ucdavis.edu/~savrasov/Projects/Teaching/2002FallPhys121/ProblemSolving3.pdf
http://www.physics.ohio-state.edu/~kass/P132/P132_ch28.pdf

 

[CWatters]

nsaspook - I'm not sure what point you are making by raising the issue of the internal resistance of the battery?

I think it's quite reasonable to decide that in some cases the internal resistance of the battery is negligible and that allows you to treat components connected to the battery as being in parallel with it.

Real world wire also has resistance and if you had to take that into account all the time you could never wire up anything in parallel.

 

[nsaspook]

nsaspook - I'm not sure what point you are making by raising the issue of the internal resistance of the battery?

I think it's quite reasonable to decide that in some cases the internal resistance of the battery is negligible and that allows you to treat components connected to the battery as being in parallel with it.

Real world wire also has resistance and if you had to take that into account all the time you could never wire up anything in parallel.

It might be reasonable to assume that (being in parallel) but I just think it's a sloppy way of viewing a simple loop circuit of series connected components. Once you start dealing with circuits with power flows greater than a few hundred watts the "negligible" series resistances become critical factors and it becomes important to use the correct methodology even with a simple thing like how to connect a wire for best battery performance with true parallel circuits.

http://www.smartgauge.co.uk/batt_con.html