I know how series and parallel circuits work and I know the rules for resistance, current, voltage, etc. I just don't know why my numbers aren't adding up in this question. When I apply the power equation P=IE to find total power I get a different number then if I add up each of the power at each resistor. They should both be the same right? What am I doing wrong?

 

Yes, they should be the same. So either the numbers in the table are not all correct or you are not using them correctly. You show how you are using them, but not how you came up with them in the first place, so if any of the numbers in the table are wrong, how can we possibly tell you what you are doing wrong?

First scan your answers and see if they all even make sense. Does it make sense that you have 10A flowing into the positive terminal of a 150V power supply (when that is the only power source in the circuit)?

Now, I should probably ask if you are using conventional current or electron current in your course.

Leaving that aside, look at your own claims. You say that the voltage across R4 is 50V. But then you say that the voltage across R2 and R3 are each 50V. So what is the voltage across the combination of R2 and R4 (i.e., from the top rail above R2 to the bottom rail below R3? How does this compare to the voltage from the top rail above R4 to the bottom rail below R4?

How did you come up with the value for R4?

 

My answers are written in ink. The other values (first 3 resistors and I1 and I2 for current) are given by whoever came up with the question.

10A would be flowing back to the positive side because it had 10A to start at I1. Because I2 is 5A going through R4 then the current through R2 and R3 would also be 5A since they are in parallel with each other (R2 & 3 is parallel with R4) and so they combine back to 10A since its back into a series circuit (where I1=I2=...). So I first found the voltage through R1 using Ohms law E=IR so (10A)(10 ohms)= 100 volts across R1. For the voltage across R2 again using ohms law and the current being 5A through that branch, (5A)(10 ohms)= 50 volts across R2. Since the resistance is the same for R3 and current is the same (in series with R2) R3 is again 50V.

Because R2 and R3 are in parallel with R4, then I said 50V is going to R4 because E1=E2=E3... in a parallel circuit. Since there is 5A flowing in that branch then using Ohms law again to find the resistance for R4 R=E/I = 50/5 = 10 ohms. For total voltage across the circuit, isn't it just the voltage across the first resistor plus the voltage across the parallel circuit, so 100+50 = 150 volts? This is where I'm not 100% sure that's right. But using that to find total power P=IE = (10A)(150V) = 1500 watts. Finding the power individually for each resistor I used P=IsquaredR. Since they are all the same amperage and resistance then they all are 250 watts: (5squared)(10)= 250 watts. Adding them all up I get 1750 watts which doesn't equal P=IE for the total circuit.

You mentioned combination voltage? For R2 and R3 it would just be 100 volts (voltages added in series). R2 and R4 combination, since its parallel would also be 100 volts. But wait I said 50 volts! So this is where I'm confused. Would that mean then that R2 and R3 should be 25 volts each so that it is 50 across R4? But then Ohms law doesn't add up for those resistors. E=IR= (5volts)(10 ohms)= 50 volts

I am not sure what you mean by conventional and electron current

 

R4 is 20 ohms, with 5amps, makes 100V across it, thats 500W.

R2 and R3 total 20 ohms, @ 5 amps also 500W,

R1 has 10 amps @ 10 ohms so it has 100V across it, and 1000W,

thats 2000W total, 200V supply.

 

I see my error now I think. The resistance of R2 and R3 needed to be added together since they are in series. So 50+50 is 100V. Since they are in parallel with R4 then the voltage across R4 is also 100V. Is that right?

 

Because R2 and R3 are in parallel with R4, then I said 50V is going to R4 because E1=E2=E3... in a parallel circuit.

Here is where your problem is. R2 and R3 are NOT in parallel, they are in series. What if R2 had been 5Ω? Then you would have had 25V across it and 50V across R3. How would you have reconciled your claim that E1=E2=E3?

You mentioned combination voltage? For R2 and R3 it would just be 100 volts (voltages added in series). R2 and R4 combination, since its parallel would also be 100 volts. But wait I said 50 volts! So this is where I'm confused. Would that mean then that R2 and R3 should be 25 volts each so that it is 50 across R4? But then Ohms law doesn't add up for those resistors. E=IR= (5volts)(10 ohms)= 50 volts

You are starting to see the light. By why are you trying to insist that 50V is across R4? You've already determined that 50V is across R2 and that 50V is across R3. These are in series, so the voltages add. THIS is then the voltage that is across R4. Knowing that R4 has 5A flowing through it, what does the value of R4 have to be?

I am not sure what you mean by conventional and electron current

If you have a 12 V battery with a 1Ω resistor across it, what direction does the current flow? Into or out of the positive terminal?

 

I see my error now I think. The resistance of R2 and R3 needed to be added together since they are in series. So 50+50 is 100V. Since they are in parallel with R4 then the voltage across R4 is also 100V. Is that right?

We cross posted. Yes, you have it now. Congratulations. Hopefully you can see that by not just giving you the answer but, instead, making you struggle with it a bit that you have probably learned quite a bit.

 

R4 is 20 ohms, with 5amps, makes 100V across it, thats 500W.

R2 and R3 total 20 ohms, @ 5 amps also 500W,

R1 has 10 amps @ 10 ohms so it has 100V across it, and 1000W,

thats 2000W total, 200V supply.

Would you PLEASE stop just posting answers to peoples' problems!