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

In summary, the conversation discusses the differences between using P=IV and P=I^2*R to calculate the power dissipated in a resistor. It is explained that both equations can be used, but P=I^2*R is generally the more accurate option. The conversation also mentions Ohm's Law and how it relates to these equations. Finally, the conversation provides an example of using these equations to calculate power in a specific scenario.
  • #1
pietastesgood
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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!
 
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  • #2
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
 
  • #3
Aha! I understand now, thanks!
 

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

What is the difference between P=I^2*R and P=IV?

The equations P=I^2*R and P=IV are both used to calculate power in electrical circuits. However, they differ in terms of what variables are used. In P=I^2*R, I represents current and R represents resistance. In P=IV, I represents current and V represents voltage.

Which equation should I use to calculate power in a circuit?

The choice of which equation to use depends on the information you have available. If you know the current and resistance in a circuit, you can use P=I^2*R. If you know the current and voltage, you can use P=IV. It is important to use the correct equation to ensure accurate calculations.

Can I use P=I^2*R and P=IV interchangeably?

No, these equations cannot be used interchangeably. They are two different equations that represent different aspects of power in a circuit. Using the wrong equation could result in incorrect calculations.

What does P=I^2*R and P=IV represent in a circuit?

In both equations, P represents power. Power is the rate at which energy is transferred or used in a circuit. In P=I^2*R, I represents current and R represents resistance, so the equation is showing the relationship between current, resistance, and power. In P=IV, I represents current and V represents voltage, so the equation is showing the relationship between current, voltage, and power.

Are there any limitations to using P=I^2*R and P=IV in circuit calculations?

Yes, these equations have limitations and are most accurate when used in simple, direct current (DC) circuits. They may not accurately represent power in more complex circuits with alternating current (AC) or other factors, such as capacitance and inductance, that affect the flow of electricity.

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