You probably meant to write you SHOULD add that to the 30.
Anyway
you need to add that to the 30v

Because V1 is in series with the 120 volt drop across the 12 ohm resistor.

 

Does this sketch help?

 

is r = 60 and r3 =20?

 

In a) R = 4

Did my sketch help or did you solve my equation for Rp (Rp=3) ?

Either way the arithmetic falls out very easily.

 

i am soo dumb lol, i am not getting it, your sketch is helping me out but i dont know how to get rp, rp is (r1*r2)/(r1+r2) but i dont have r values. I appreciate all of your help and deidcation

 

In my top sketch

So the 120 + 30 = 150 volts is distributed across the voltage divider formed by 12 and Rp
such that 30/150 = Rp/(12+Rp)

This is an equation in Rp that you can solve to get Rp=3

Now substitute R and 3R for r1 and r2 in your parallel formula and equate to Rp =3
You now have an equation in R you can solve to get R = 4

Alternatively

In the bottom sketch note that the current divides in inverse proportion to the resistors so there is 3 times the current in the R resistor as in the 3R one.

thus total current is I plus 3I =4I

This must be = to the 10 amps incoming 4I = 10 > I = 2.5, 3I = 7.5

Since there is 30 volts across the single R resistor and 7.5 amps through it, Ohms law give R = 30/7.5 = 4 as before.

 

the secong way i got it, the cheat way but my problem is the algebra, solving that equation, and the r that i gave before was wrong i divided by the total v instead of the v going across

 

I'm glad you are beginning to see the light.

You should now try it another way to reinforce the concepts.

The 12 Ohm and Rp are in series so pass the same current.

So there is 10 amps through Rp and we are told there is 30 volts across it.

So by Ohms law Rp = 30/10 = 3, as before.

Get used to viewing the same circuit different ways.

Now have a go at part b). My sketch gives you all you need.

 

for part b i subtracted 1200w from the 12Ω from the total leaving me with 375. than i divided it by 4 leaving me 93.75 so r = 93.75 and r3 = 281.25 am i correct?

 

the remaining power is 1575 - 1200 = 375 correct.

Thus = (3I)^*2R + (I)^2*3R = 375

ie 9Isquared times R plus I squared times 3R = 375

ie R(12Isquared) = 375

but I = 2.5 amps

ie R(75) = 375

ie R = 5

If you have trouble with algebra, lay it out in small steps like this. Don't try to do too much in one go.

 

got it thank you for your help

 

Cheers, Keep practising.