Electric Radiator: P=750W, V=230V, R=70.54 Ohms

[chawki]

Homework Statement

An electric radiator which is an ordinary constant resistor emits a heating power of
750 W at a mains supply voltage of 230 V.

Homework Equations

What is the total heating power in each respective instance when two such radiators are connected a) in parallel, and b) in series to the 230 V
supply voltage?

The Attempt at a Solution

P=750 W
V=230 V
we calculate R
P=V²/R
R=230²/750
R=70.54 Ohms

when 2R are in parallel:
Req=R/2 = 70.54/2 = 35.27 Ohms
P=230²/35.27 = 1499.85 approximately 1500 W

when 2R are in series:
Req=2R
P=230²/(2*70.54)
P=375 watt

 

[tiny-tim]

hi chawki!

yes, that's correct

except …

… P=230²/35.27 = 1499.85 approximately 1500 W

it isn't approximately 1500 W, it's exactly 1500 W

it's time you learned how to do this without finding R …

P = V²/R, and you know that the new resistance is either R/2 or 2R, so the new power will be either twice or half the original power, ie 750*2 W or 750/2 W, ie 1500 W or 375 W exactly

isn't that easier, and less likely to lead to errors? ​

 

[chawki]

you are very right, but i couldn't understand the tip
and I'm used to use R
i tried I but it didn't help a lot..always that small error, but well, in my answer using R i just round it to 1500
it should be ok ?

 

[tiny-tim]

it should be ok ?

yes, but it takes up time in the exam …

the principle is very easy …

you know the formula is P = V²/R …

if you're only changing R, then obviously if you multiply R by 2, you'll divide P by 2

(alternatively, if you keep R the same, and multiply V by 2, then you'll multiply P by 4)

you don't need to know R (or in the second case, V) to do it!

some courses call this "dimensional analysis"

 

[chawki]

yes, but it takes up time in the exam …

the principle is very easy …

you know the formula is P = V²/R …

if you're only changing R, then obviously if you multiply R by 2, you'll divide P by 2

(alternatively, if you keep R the same, and multiply V by 2, then you'll multiply P by 4)

you don't need to know R (or in the second case, V) to do it!

some courses call this "dimensional analysis"

so R will goes away?
can you write that step by step and i will understand it

 

[tiny-tim]

yes …

P₁ = V²/R₁

P₂ = V²/R₂

So P₂/P₁ = R₁/R₂

 

[chawki]

yes but then what? we will still have to find R
also, if you can, please check this if it's correct https://www.physicsforums.com/showthread.php?t=481152