Calculating total circuit resistance

[Jalisi]

Homework Statement

Calculate the total resistance of the circuit.
Calculate the potential difference across each of the resistors.

http://img849.imageshack.us/img849/2190/hw1v.jpg

Homework Equations

Series resistors= R_T=R1+R2+R3
Parallel resistors = 1/R_T=1/R₁+1/R₂+1/R₃

V=iR or i=V/R
V=voltage i=current R=Resistance

The Attempt at a Solution

I'm trying to find the "groups" in the circuit so I can calculate the smaller parts them combine into a whole.

I started by calculating R5 and R6, which are parallel. 1/600+1/200=4/600=600/4=150Ω

My problem starts here. I'm not quite sure which resistors are in parallel and which are in series. I calculated R2, R4, and R7 as being parallel. Thus 1/500+1/1000+1/2000=7/2000=2000/7= 285.7Ω

Now that I have the parallel groups solved, I can look at the resistors in series so: 200Ω+ 150Ω +285.7Ω + 100Ω = 735Ω

Would that be correct for the total resistance?

If so, then to find the total current, use i=V/R so i=25v/735Ω = 0.034A

And from there I have total voltage, current, and resistance so it should be fairly easy to calculate each potential difference.

Thanks so much for any help provided.

 

[SammyS]

Homework Statement

Calculate the total resistance of the circuit.
Calculate the potential difference across each of the resistors.

http://img849.imageshack.us/img849/2190/hw1v.jpg

Homework Equations

Series resistors= R_T=R1+R2+R3
Parallel resistors = 1/R_T=1/R₁+1/R₂+1/R₃

V=iR or i=V/R
V=voltage i=current R=Resistance

The Attempt at a Solution

I'm trying to find the "groups" in the circuit so I can calculate the smaller parts them combine into a whole.

I started by calculating R5 and R6, which are parallel. 1/600+1/200=4/600=600/4=150Ω

My problem starts here. I'm not quite sure which resistors are in parallel and which are in series. I calculated R2, R4, and R7 as being parallel. Thus 1/500+1/1000+1/2000=7/2000=2000/7= 285.7Ω

Now that I have the parallel groups solved, I can look at the resistors in series so: 200Ω+ 150Ω +285.7Ω + 100Ω = 735Ω

Would that be correct for the total resistance?

If so, then to find the total current, use i=V/R so i=25v/735Ω = 0.034A

And from there I have total voltage, current, and resistance so it should be fairly easy to calculate each potential difference.

Thanks so much for any help provided.

Hello Jalisi . Welcome to PF !

Your analysis of the circuit has several errors.

Lets look at the circuit starting with the "big picture", and progressing down to the small details.

First of all, there's just one voltage source. Let's start there.

Any current passing through the battery must also pass through R₁. From there the current branches off in some complicated way through the rest of the resistors. It then returns to the battery, where the process starts all over again.

So, the voltage source is in series with R₁ and in series with some resistance that's equivalent to the combination of all the other resistors.​

Now for a little more detail:

Current passing through R₁ then splits and goes through either R₂ or through a combination of the rest of the resistors R₃ through R₇ .

So we have R₂ in parallel combination of rR₃ though R₇ .​

Current which passes through R₁ but not through R₂ must pass through some combination of R₄ thru R₇ before it all comes back together and passes through R₃ -- after which it joins up with the current from R₂ and returns to the voltage source.

So R₃ is in parallel with the combination of the resistors, R₄ thru R₇​

...See if you can take it from there.

 

[CWatters]

I started by calculating R5 and R6, which are parallel. 1/600+1/200=4/600=600/4=150Ω

You are on the right lines upto this point. The trick is to redraw the circuit at each step until you get used to doing it so..

Redraw the circuit with R5 and R6 replaced by a single resistor marked "R5//R6".

Then it should be obvious that R7 is in series with R5//R6. So redraw the circuit with one resistor replcaing R5//R6 and R7 and marked "(R5//R6) + R7".

Then you will see that the resistor "(R5//R6) + R7" is in parallel with another resistor. I'll let you work out which one and continue from there.

 

[rollingstein]

I calculated R2, R4, and R7 as being parallel.

Mistake.

 

[rollingstein]

A Tip: Two Resistors are in parallel only if you can connect both their ends to each other without any intervening resistors.

 

[Jalisi]

SammyS and CWatters -

Thanks for helping me figure out exactly where I was messing up and how. It took a few more attempts to really apply what you were two were talking about, then a couple more to get the match correct, but in the end I got the circuit solved. Thanks for putting me back on the correct path!

rollinstein- Thanks for the tip. That will come in handy over the next few chapters.

Thanks again all!