Why Do P=IV and P=I^2*R Yield Different Results in This Case?

[pietastesgood]

Homework Statement

Part f. Calculated current = 0.5 A. Voltage = 30 V. Resistance = 40 Ω

Homework Equations

P=IV
P=I^2*R
P=V^2/R

The Attempt at a Solution

I've been curious about this for a while. Sometimes when I am asked to find the power dissipated through a resistor, and I use P=IV, it doesn't yield the same answer as if I used P=I^2*R, which is generally the correct answer. This is such an example. P=IV yields 15 W, while P=I^2*R yields 10 W, which is the correct answer. Can anyone explain this? And under which circumstances should I use P=I^2*R, and under which circumstances should I use P=IV? Thanks in advance!

 

[ehild]

The power dissipated in a resistor is P=IV where V is the voltage across the resistor and I is the current through the resistor. Ohm's Law states that the voltage across a resistor of resistance R is V=IR. So P=IV can also be written as P=I(IR)=I²R.

30 V is the voltage across the chain of the 40 Ω and 20 Ω resistors. It is 20 V across the 40 Ω resistor when the switch is closed for a long time.

ehild

 

[pietastesgood]

Aha! I understand now, thanks!