Solving Electrical Circuits: Series & Parallel Components

[Aikenfan]

Homework Statement

Homework Equations

P = IV
V = IR

The Attempt at a Solution

I know how to solve the problem once i figure out which parts are parallel and which parts are series. So would it be R2 and R3 are in parallel and R4 is series, but what about R1? i have done a problem similar to this but without the R1 on the side (shown in the picture above)...if anyone can explain to me what is different about this, i would really appreciate it.

 

[Dick]

I think you misspoke. R2 and R3 are in series. R4 is in parallel with them. R1 is in turn in series with the combination of the other 3. Yes?

 

[Aikenfan]

yeah, I got that a little mixed up there! thank you for the help!

 

[Aikenfan]

I think I've got it now, if anyone can double check my work, it would be greatly appreciated (still not sure if I am doing it correctly, but i think I've got the idea)

 

[Dick]

Well, Rt looks good. Lots of problems elsewhere. Why on Earth would you say V1=120?? Since the sum of the voltages around a loop is zero? And how could I1 not equal It? Where is the rest of the current going?

 

[Aikenfan]

I don't really know, I am going to go back and try again: we just learned this today, so I am really new at this.

 

[Aikenfan]

so V1= 0 and I1 = 0??

 

[Dick]

so V1= 0 and I1 = 0??

V1 is not 0V and it's not 120V. Are you just guessing? What is the total current running through the circuit? Hint: You got that right. How much of it goes through R1? THINK about that!

 

[Aikenfan]

all of it. 21.4

 

[Dick]

all of it. 21.4

That's better. Now you know I and R for R1. Find V1. Now continue stepping through the circuit...

 

[Aikenfan]

What I've got so far:

 

[Dick]

Ok. Now do V4. Sum of voltages around a closed loop is zero. You are keeping track of signs in your head, right?

 

[Aikenfan]

so V4 = 85.6 because it is in parallel

 

[Dick]

It's NOT in parallel with R1! It's in series! Draw a loop through the battery including R1 and R4. Sum of all those voltages better be zero.

 

[Aikenfan]

well, since it is in series, wouldn't that make I4 = 21.4? so that would make V4 = 42.8

 

[Dick]

No. It's not really in 'series'. Part of the 21.4A flows through R4 and part of it flows thru the R2 R3 combo. Concentrate on V4. Concentrate on the loop I suggested. Vbattery+V1+V4=?

 

[pugfug90]

R(2,3,4) are in series with R1.. That means that V1+V(2,3,4)=Vt.. Therefore, V(2,3,4) equals 34.4V (120-85.6)..And in a parallel circuit, voltage is the same across each !branch.. That means that 34.4V=V(2,3,4)=V4=V(2,3)

And the parentheses is used to indicate how they are when combined..

Now that I've showed you V4, you can get I4..

 

[Aikenfan]

V4 = 34.4, am i understanding that correctly?
34.4 +85.6 = 120
and then V2 = 34.4 and V3 = 34.4

 

[Dick]

Nooooo. V2+V3=34.4V. Please review Kirchoff laws, ok?

 

[Aikenfan]

Sorry for all of the questions, i am not very familiar with this material, we only touched on it a little today for the first time... i will go look up Kirchoff laws and see if that will help some.

 

[pugfug90]

I'm pretty sure that V4 as 34.4V is right.. and V2 and V3 definitely aren't..

In a parallel circuit, all !branches have the same voltage.. That means that the combined voltage (added) of R2 and R3 equal to the same voltage as R4's voltage..

You have R4, V4, figure out I4..

I(t)=I1=I(2,3,4).. In a combo circuit, total current I(t) is equal to/same in all series resistors (I1), or the sum of all current in a parallel (I2+I3+I4=It)..

Now if you can figure I4..
It-I4=I2+I3..
and I2+I3 is the same thing as I(2,3) since in a series circuit, current is the same throughout...

 

[Dick]

I'm pretty sure that V4 as 34.4V is right.. and V2 and V3 definitely aren't..

In a parallel circuit, all !branches have the same voltage.. That means that the combined voltage (added) of R2 and R3 equal to the same voltage as R4's voltage..

You have R4, V4, figure out I4..

I(t)=I1=I(2,3,4).. In a combo circuit, total current I(t) is equal to/same in all series resistors (I1), or the sum of all current in a parallel (I2+I3+I4=It)..

Now if you can figure I4..
It-I4=I2+I3..
and I2+I3 is the same thing as I(2,3) since in a series circuit, current is the same throughout...

Be careful, pugfug. He's new at this game and doesn't need to be confused. I2=I3! Not I2+I3=I(2,3)!?

 

[Aikenfan]

so the voltage for V2 is 17.2 and V3 = 17.2--combined voltage of R2 and R3 = R4?

 

[Dick]

so the voltage for V2 is 17.2 and V3 = 17.2--combined voltage of R2 and R3 = R4?

How can V2=V3 when they have the same current through them and different resistances??! Review Kirchoff, take a break and try the problem again.

 

[Aikenfan]

V4 = 34.4
I4 = 17.2
R4 = 2
P4 = 591.68

 

[Dick]

Ok. What's the relation between I2 and I3? What is their relation to I4 and I1?

 

[Aikenfan]

I2 and I3 are the same

 

[Aikenfan]

Would I subtract I4 = 17.2 from I1 = 21.4 to get 4.2 as I2 and I3?

 

[pugfug90]

Yay!
I think.
Now the next steps..

And to confuse yourself less.. It wouldn't make any difference, but I think it's more proper to say that you subtract I4 from It..

 

[Aikenfan]

Okay! i think i have got it now:

 

[Dick]

Check your work. Is the sum of the power in each resistor equal total power? No! It's not! Find the problem(s). It's not a major disaster.