Calculating Current and Voltage in a Circuit with Multiple Resistors

[nothing909]

How do I find the current across the 5Ω resistor?

I worked out the supply current by simplifying the circuit down.
I then went on to work out the voltage across the 3Ω resistor using the supply current.
I then used that voltage to then work out the voltage across the 4Ω resistor.

Now I'm stuck. How do I work out the voltages of the other 3 resistors and get the current across the 5Ω resistor?

 

[donpacino]

do you know how current division work?
or you can use ohms law to find the voltage drop across the first resistor

 

[nothing909]

I don't know how current division work, and what do you mean by using ohms law to find find the voltage across the first resistor?

 

[donpacino]

you know the current through the 3 ohm resistor, so you should be able to calculate the voltage drop across it. then use the supply voltage to figure out the voltage across the 5 ohm resistor.

 

[nothing909]

I calculated the voltage across the 3Ω resistor which I show in the last picture. After I worked out the voltage across the 3Ω resistor, I subtracted it from the supply voltage to work out the 4Ω resistor.

Can you explain how I work out the current and voltages for the rest of the resistors?

 

[donpacino]

if you know the voltage across the 4 ohm resistor, then you know the voltage across the 5 ohm resistor. you also know the voltage across the series combination of the 2 and 1 ohm resistors.

 

[nothing909]

I've just started my engineering course in and I've not did this kind of stuff for a long time. Can you tell me the voltage across 5Ω resistor so I can understand what you mean.

 

[donpacino]

the 5 ohm resistor and the four ohm resistor are in parallel...

 

[nothing909]

So the voltage across the 4Ω resistor is the same as the 5Ω resistor?

 

[donpacino]

yes, due to the fact that they are in paralell.
you made an error in your work

edit: disregaurd what i said , you skipped a step in your work and i thought u made an error

 

[nothing909]

I'm sorry for going on and maybe I'm asking stupid questions, but I really need to know this

I don't understand what you mean when you say that I've made a calculation error. Where did I do this? Which picture shows this?

I know that after working out the voltage of the 5Ω resistor, it allows me to .work out the current and that's the question answered, but can you please explain how I then work out the voltages and currents of the 2Ω and 1Ω resistors.

 

[donpacino]

I'm sorry for going on and maybe I'm asking stupid questions, but I really need to know this

I don't understand what you mean when you say that I've made a calculation error. Where did I do this? Which picture shows this?

I know that after working out the voltage of the 5Ω resistor, it allows me to .work out the current and that's the question answered, but can you please explain how I then work out the voltages and currents of the 2Ω and 1Ω resistors.

thats fine, no need to apologize...

you did not make an error. I thought you added 1/Rt and 3 ohm.

so the 2 and 1 ohm resistors are in parallel with the 5 ohm resistor. SO you can either use voltage division, or use the same process you did before

 

[nothing909]

How do I do voltage division?

 

[donpacino]

How do I do voltage division?

https://en.wikipedia.org/wiki/Voltage_divider

its a shortcut for finding the voltage across individual resistors in a series chain.

lets say you have 2 resistors R1 and R2 in series and a voltage Vin across them

the current is Vin/(R1+R2)
then to get the voltage across either of the resistors, you multiply the current by the resistance.

so Vr1=Vin*R1/(R1+R2)

the same goes for R2.
make sense?

 

[donpacino]

current division, which I talked about earlier, can be derived in a similar way...

two resistors R1 and R2 in parralel with current Iin going into them

the voltage is
V=Iin*R1*R2/(R1+R2)

then voltage over resistance gives you current

so IR1=Iin*R2/(R1+R2)

 

[nothing909]

Okay, maybe a dumb question, but I understand voltage division now, but what would be the value of Vin for the 1Ω and 2 Ω resistor?

 

[William White]

tip

draw circuits using only horizontal and vertical lines.another tip

draw circuits going left to right (rather than as a loop) (this is a very common, commonsense way to draw circuits)

start on the left with the positive terminal of the battery. imagine walking along the wire. that's a straight line. when you get to a junction you can turn left, right, or keep going. draw like this until you get to the negative terminal of the battery which is on the far right of your page. Now, what is in parallel and what is in series very clearly defined. This method is very useful as circuits become more complex and it is essential to know what is in parallel with what just by glancing at the diagram.this way you can get a much clearer picture of what is going on, something like this, but draw it for yourself.

when it is like this you can quikly work out the total current; and the current flowing through each resistor

 

[donpacino]

Okay, maybe a dumb question, but I understand voltage division now, but what would be the value of Vin for the 1Ω and 2 Ω resistor?

vin is the voltage across the two resistors... so what is the voltage across the two resistors?

 

[nothing909]

Is the voltage across the two resistors 42.09v? or is it just 60v like the supply voltage. i don't really know

 

[donpacino]

so while what william said is not always possible, you should follow that advice, even if you have to redraw a circuit. it will help

a good example is this question posed a few days ago
https://www.physicsforums.com/threads/equivalent-resistance-between-a-and-d.829415/#post-5210284

while the circuit looks confusing, its simply 3 resistors in parallel. It simply looks confused due to the way it is drawn.

 

[donpacino]

Is the voltage across the two resistors 42.09v? or is it just 60v like the supply voltage. i don't really know

so the 60V goes across the 3 ohm resistor as well as the 1 and 2 ohm resistors.
you want to use the voltage that is DIRECTLY across the 1 and 2 ohm resistors.

 

[nothing909]

Okay, I'm sorry, I don't understand what you mean. Can you please just tell me the voltage across the two resistors so I can understand?

Also, is the 4Ω, 5Ω and 1Ω resistor all in parallel with each other? If so, does that mean the 1Ω resistor has a voltage of 17.09 like the rest in parallel?

 

[William White]

Okay, I'm sorry, I don't understand what you mean. Can you please just tell me the voltage across the two resistors so I can understand?

Also, is the 4Ω, 5Ω and 1Ω resistor all in parallel with each other? If so, does that mean the 1Ω resistor has a voltage of 17.09 like the rest in parallel?

1) Draw the diagram properly - so it looks like something I have done. Do it very carefully and neatly. If you do it properly, you will know, just by looking what is in series and what is in parallel!

2) You can then replace all the resistors with a single resistor. There are rules for working out equivalent resistances, which you need to know. So you will have two drawings, one with all your resistors (from step one) and one with a single resistor. The circuit that contains ONE resistor that has the same resitance as all your resistors in the other circuit. They are the same as far as the battery is concerned.

3) Now you can work out the total current through this single resistor using ohms law. This current is the current leaving your battery in your original drawing.

4) Now go back to your original drawing, with several resistors.

4) Work out the volt drop (using ohms law) across each resistor.

5) Done.

Try to do this step by step. When you get stuck on a step, ask.

 

[nothing909]

Okay I've did all that. I reduced all the resistors into one single resistor and then worked out the supply current using ohms law as you can see in the working.

I understand how to work out the voltages for the 3Ω, 4Ω and 5Ω resistor, but I don't understand how to work out the voltages for the 2Ω and 1Ω resistor.

 

[donpacino]

Okay I've did all that. I reduced all the resistors into one single resistor and then worked out the supply current using ohms law as you can see in the working.

I understand how to work out the voltages for the 3Ω, 4Ω and 5Ω resistor, but I don't understand how to work out the voltages for the 2Ω and 1Ω resistor.

you can work it out the SAME way you've been doing it before. look at the drawing William produced. look up the definition of series and parallel and tell me what relationship those resistor have with the four and 5 ohm resistors.

 

[William White]

Okay I've did all that. I reduced all the resistors into one single resistor and then worked out the supply current using ohms law as you can see in the working.

I understand how to work out the voltages for the 3Ω, 4Ω and 5Ω resistor, but I don't understand how to work out the voltages for the 2Ω and 1Ω resistor.

the volt drop across a resistor is ohms law

V =IR

you know R (it is given) so you need to know what I is
Do you know how the current is divided between resistors in parallel?

If you had a one ohm and two ohm resistor in parallel and the total current was 3A what current is going through each resistor? So then what is the volt drop across each resistor?

 

[nothing909]

donpacino told me to do voltage division. i understand the concept but i don't understand what the voltage across the two resistors are supposed to be.

i know you're not supposed to give the answers, but it'd make much more sense to me if one of you just told me the voltages across the both resistors so i can make sense of it and if i can't i'll ask again

 

[William White]

you don't know what the voltage across the resistors are because you have not drawn it properly!

have you followed the step-by-step instructions I gave you?

ie have you looked at my drawing and drawn your own?
- unless you have the mental insight of a genius its essential to always - always - draw the problem clearly and neatly. Once this is done, you will find the problem virtually solves itself. The scribble you provided is creating you more problems than it is solving!

 

[donpacino]

donpacino told me to do voltage division. i understand the concept but i don't understand what the voltage across the two resistors are supposed to be.

i know you're not supposed to give the answers, but it'd make much more sense to me if one of you just told me the voltages across the both resistors so i can make sense of it and if i can't i'll ask again

what is the relationship between the 5 ohm resistor and the four ohm resistor. that should give you some insiight into the relation between the four ohm resistor and the (1 & 2) ohm resistors.

 

[nothing909]

no, i have followed the steps and redrew it but i still don't get it

 

[donpacino]

you don't know what the voltage across the resistors are because you have not drawn it properly!

have you followed the step-by-step instructions I gave you?

ie have you looked at my drawing and drawn your own?
- unless you have the mental insight of a genius its essential to always - always - draw the problem clearly and neatly. Once this is done, you will find the problem virtually solves itself. The scribble you provided is creating you more problems than it is solving!

william at this point simply drawing it out is not going to solve the problem, as Op has your drawing to look at

 

[donpacino]

no, i have followed the steps and redrew it but i still don't get it

check post 29

 

[nothing909]

what is the relationship between the 5 ohm resistor and the four ohm resistor. that should give you some insiight into the relation between the four ohm resistor and the (1 & 2) ohm resistors.

the

check post 29

the 4 ohm resistor is in parallel with the 5, yeah, so are all 3 of them in parallel with each other?

 

[donpacino]

the

the 4 ohm resistor is in parallel with the 5, yeah, so are all 3 of them in parallel with each other?

yup! if you have any doubts, look up the definition of parallel resistors. eventually it will be intuitive

 

[William White]

no, i have followed the steps and redrew it but i still don't get it

okay, so you know the total currentif you have drawn the circuit properly, you will see that the current is going through three parallel paths, top middle bottom

do you know the rules for dividing the current through the top middle and bottom paths?if the top path is 3ohms
the middle path is 4 ohms
and the bottom path is 5 ohms

and the total current is 14A

what current is going though each path? The lower the resistance the MORE current, so expect the largest amount to go through the top path, and the least in the bottom path.

when you know these currents, tell me what they are.

 

[nothing909]

okay, thank you, but i feel like an idiot still asking question when u guys have explained all this like 10 times.

if the voltage for the 4 ohm resistor is 17.09v, that means the voltage across the 5 resistor and the 1 ohm resistor are all 17.09, yeah? so what's the voltage across the 2 ohm resistor?

 

[nothing909]

okay, so you know the total currentif you have drawn the circuit properly, you will see that the current is going through three parallel paths, top middle bottom

do you know the rules for dividing the current through the top middle and bottom paths?if the top path is 3ohms
the middle path is 4 ohms
and the bottom path is 5 ohms

and the total current is 14A

what current is going though each path? The lower the resistance the MORE current, so expect the largest amount to go through the top path, and the least in the bottom path.

when you know these currents, tell me what they are.

i don't understand how to work it out. do i need to just do something like voltage division but instead with current?

 

[donpacino]

okay, thank you, but i feel like an idiot still asking question when u guys have explained all this like 10 times.

if the voltage for the 4 ohm resistor is 17.09v, that means the voltage across the 5 resistor and the 1 ohm resistor are all 17.09, yeah? so what's the voltage across the 2 ohm resistor?

close but no... that 19.09 V is across the series combination of the 1 and 2 ohm resistors.

and again don't feel bad for asking questions

 

[nothing909]

so 17.09 is the Vin? so i just do 17.09 x 1/3 and 17.09 x 2/3 and that'll give me the voltages for both of the individual resistors?

 

[William White]

i don't understand how to work it out. do i need to just do something like voltage division but instead with current?

so, this is the key to solving the problem;

the current through the resistor is inversly proportional: less resistance more current.

you have 14A

If you have a 2+1 = 3 ohm resistance in the top path. 4 ohm resistor in the middle
5 ohm in the bottom

can you show that the currents are
6A
4.5A
3.5A

?

 

[nothing909]

so, this is the key to solving the problem;

the current through the resistor is inversly proportional: less resistance more current.

you have 14A

If you have a 2+1 = 3 ohm resistance in the top path. 4 ohm resistor in the middle
5 ohm in the bottom

can you show that the currents are
6A
4.5A
3.5A

?

look at my above post. is that right what i said?

 

[William White]

yes, the voltage across the three parallel paths is 17.9 V...

so you know the resistances...so what are the currents through each path?

 

[nothing909]

yes, the voltage across the three parallel paths is 17.9 V...

so you know the resistances...so what are the currents through each path?

The currents are just I=V/R after I've worked out the voltages, yeah?

 

[donpacino]

so 17.09 is the Vin? so i just do 17.09 x 1/3 and 17.09 x 2/3 and that'll give me the voltages for both of the individual resistors?

exactly

 

[William White]

Yes,

and you have told me the voltage drop across the three paths - it is 17.9 V

so now tell me the current through each resistor...

 

[nothing909]

the current across the 4 ohm resistor is 71.4
the current across the 5 ohm resistor is 89.55
the current across the 1 ohm resistor is 5.97
the current across the 2 ohm resistor is 5.97

 

[William White]

you have already told us the correct TOTAL current, which is 14A

all your currents must add up to this! you have multiplied rather than divided! i = v / R

you have 17.9V across a 5 ohm resistor...that is 3.58 A

what are the others?

 

[nothing909]

wait, i don't understand. is my answer for the 1 and 2 ohm resistors correct?

i did for the 1 ohm resistor: 17.91x1/3, then I=5.97/1

for the 2 ohm resistor : 17.91x2/3, then I=11.94/2

 

[William White]

yes;

The 1 and 2 ohm resistors are in series - the current through them is the same.

therefore they are equivalent to a 3 ohm resistor

17.9 V / 3 ohm = 6A

 

[nothing909]

yeah sorry

for the 4 ohm it's 4.48
for the 5 ohm it's 3.58