Power rating of a heater in the same outlet as a hair dryer

  • Thread starter OmegaFury
  • Start date
  • #1
28
0

Homework Statement


A heater is plugged into the same 120-V AC outlet as an 800-W hair dryer. If the total rms current drawn is 16.7A, then calculate the power rating of the heater.


Homework Equations


Pav=[itex]\frac{1}{2}[/itex]I2peakR


The Attempt at a Solution


Irms=Ipeak/[itex]\sqrt{2}[/itex]
So, Ipeak=16.7A x [itex]\sqrt{2}[/itex]
Solving for R in the Pav equation: 2Pav/I2peak=R
(2 x 800W)/(16.7A x [itex]\sqrt{2}[/itex])2= 2.87 ohms.

I'm assuming that in an outlet, the heater and the dryer are in parallel, so V=V1=V2 and Itotal=I1+I2
Using ohms law V/R=I, 120V/2.86 ohms= 41.81 A. Since this is too high, I know I'm looking at this problem completely wrong. I wanted to use that to find I2, solve for R, and find the power of the heater.
 
Last edited:

Answers and Replies

  • #2
gneill
Mentor
20,909
2,858
I think you can avoid the average and peak conversions and stick to rms values.

What's the rms current drawn by the hair dryer if it uses 800W at 120V (rms)?
 
  • #3
28
0
Okay, so I use PavrmsIrms
Pavrms=800W/120V=6.67A. The rms current of the heater would be 16.7A-6.67A= 10.03A. Thus, the power rating of the heater would be 120V x 10.03A= 1203.6W. Is that correct?
 
  • #4
gneill
Mentor
20,909
2,858
Okay, so I use PavrmsIrms
Pavrms=800W/120V=6.67A. The rms current of the heater would be 16.7A-6.67A= 10.03A. Thus, the power rating of the heater would be 120V x 10.03A= 1203.6W. Is that correct?
It looks good :smile:
 
  • #5
28
0
Thanks for the help :smile:
 

Related Threads on Power rating of a heater in the same outlet as a hair dryer

  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
1
Views
3K
Replies
3
Views
12K
  • Last Post
Replies
13
Views
13K
Replies
24
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
16
Views
3K
Replies
6
Views
3K
Top