Power in electric circuits – how long will it take to cook three hot dogs?
A certain brand of hotdog cooker works by applying a potential difference of 120 V across opposite ends of a hot dog and allowing it to cook by means of the thermal energy produced. The current is 11.0 A, and the energy required to cook one hot dog is 58.0 kJ. If the rate at which energy is supplied is unchanged, how long will it take to cook three hot dogs simultaneously?
mmmm hot dogs. be sure to give me one when your’re done cooking them
Doesn’t the conductivity of the hot dog vary from brand to brand changing the resistance?
This method of cooking hot dogs actually works; I have done it many times.
If your cooker uses 120 volts and the current is 11 amperes, the total power
it uses is 1320 watts, or 1320 joules every second. If it is divided equally among
the 3 wieners, each wiener receives 440 watts, or 440 joules of energy every
second. If a wiener needs 58,000 joules to cook completely, the time needed
is 58,000 joules divided by 440 J per second, or 131.8 seconds – 2 minutes and
11.8 seconds. In actual practice, it doesn’t take much longer than this, although
the resistance of the wieners starts out relatively high, about 200 ohms each
and gradually decreases to about 100 ohms per wiener as the hot dogs cook.
But for your example here, the time required is 131.8 seconds.