Current, Power dissipation in a cord

  • #1
PeachBanana
191
0

Homework Statement



An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 1.2m (4ft ) is connected to an electric heater which draws 15.0A on a 120 V line. How much power is dissipated in the cord?


Homework Equations



P = IV
R = ρL / A
P = V^2/R

The Attempt at a Solution



First I found the power required by the heater.

P = (15.0 A)(120 V)
P = 1800 W

Next I wanted to find the power within the cords.

R = ρL / A
A = 6.45*10^-4 (∏)

R = 1.68*10^-8(1.2 m) / (6.45 * 10^-4)^2(∏)
R = 1.542*10^-2 Ω

P = V^2 / R
P = (120 V)^2 / (1.542*10^-2 Ω)

P = 9.338*10^5 W

I thought that was the power within the cords so next I:

9.388*10^5 W - 1800 W = 9.32 * 10^5 W.
 

Answers and Replies

  • #2
lewando
Homework Helper
Gold Member
1,367
144
The heater operates at 1800 W. You would think the cord Pd would be much less. Need to determine resistance of copper wire given length and diameter. Consider both wires.
 
  • #3
PeachBanana
191
0
I thought the equation R = ρL/A considered the resistance of copper. Was this the incorrect equation to use?
 
  • #4
22,321
5,201
Your main error is that the voltage drop across the cord is not 120 volts. That's the voltage drop across the heater. The voltage drop across the cord is much less. The current through each of the two wires of the cord is equal to the current through the heater. Use ohm's law to correctly calculate the potential drop across each of the wires of the cord. Or skip this step, and use P = I2R to get the power consumed in each wire of the cord.
 
Last edited:
  • #5
PeachBanana
191
0
Found the right answer to be ~7 W. Thank you.
 
  • #6
CWatters
Science Advisor
Homework Helper
Gold Member
10,545
2,317
As a check...

Resistance of No. 16 wire is about 4 Ohms per 1000 ft so 4ft would be 0.016 ohms.

However you have to double that because the length of wire is twice the length of the cord. So 0.032 Ohms round trip.

Power = I2 * R
= 152 * 0.032
= 7.2 W
 
  • #7
PeachBanana
191
0
Thank you CWatters. I got my exact answer to be 6.9 W which I rounded up to 7.
 

Suggested for: Current, Power dissipation in a cord

Replies
1
Views
382
Replies
3
Views
253
Replies
21
Views
721
  • Last Post
Replies
4
Views
558
Replies
11
Views
518
  • Last Post
Replies
1
Views
288
Replies
2
Views
2K
Top