Power Dissipation

[thais]

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Hey Guys,
I ran into this question earlier today and I'm a bit confused.

"A 12-volt battery causes current to flow through a circuit containing just two 8-ohm resistors connected in parallel. How much power is dissipated in one of these resistors?"

I answered 36 watts, my reasoning behind it being P=V^2/R. Since the Resistors are in parallel I added their inverse resulting Rtotal= 4ohms. Then, 144/4= 36watts.

However, the correct answer is 18watts. They did not add the resistors but just solved for power individually.
Could someone explain to me how does it work? Is the same amount of power dissipated on each resistor? How is that possible? Isn't there a "total power" for the entire circuit?

Thank you!!

 

[Ssina]

36W that you calculated is fot both resistors combined, the question wants each, so just divide it by 2!

 

[Pisiform]

Hey Guys,
I ran into this question earlier today and I'm a bit confused.

"A 12-volt battery causes current to flow through a circuit containing just two 8-ohm resistors connected in parallel. How much power is dissipated in one of these resistors?"

I answered 36 watts, my reasoning behind it being P=V^2/R. Since the Resistors are in parallel I added their inverse resulting Rtotal= 4ohms. Then, 144/4= 36watts.

However, the correct answer is 18watts. They did not add the resistors but just solved for power individually.
Could someone explain to me how does it work? Is the same amount of power dissipated on each resistor? How is that possible? Isn't there a "total power" for the entire circuit?

Thank you!!

Dude, you already said that the formula is P = V^2/R. So since both resistors are in parallel they both have the same voltage as that of the battery i.e. 12 Volt.

P = V^2 / R

P = 12^2 / 8 = 18W

what you did was that found the TOTAL power dissipated (by finding combined resistance) and NOT the Power dissipated in one resistor which question was asking.

 

[Erythropoietin]

^Yes

You can also find it by using the other formula
V=IR...since parallel has the same voltage, I will be 1.5
from P=IV, you get P = 18 W

 

[thais]

Thank you!!