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MCAT Physics Question - P = IV and Ohms Law

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grignardsgoblin

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P = IV and V = IR. I get these and I understand how (1) P = I^2 * R and (2) P = V^2 / R can be derived from those two equations algebraically.

What I am stupendously dumbfounded on is how the two derivatives relate to each other both qualitatively and quantitatively (in example problems).

On the one hand, (1) says that power is directly proportional to resistance, and on the other hand (2) says that power is inversely proportional to resistance. Can someone please explain to me the difference between the two? Hopefully my point of confusion is clear. Ideally a theoretical explanation and two examples. Example 1 showing why you use equation (1) and NOT equation (2), and example 2 showing why you use equation (2) and NOT equation (1).

Let me know if anything needs clarification. - gg
 

type12

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So, let's get some terms in order here:

Power: how much ENERGY a battery is able to provide to the resistor every second
Voltage: the ability to provide ENERGY should there be something to give it to. (aka, the potential to provide energy)

The ability to provide energy to a system is dependent on how many charged particles you have, and how resistant to this charge your system. Think of how, when you are lifting (h) something with a crank, every rotation is your current, and the weight of what you are moving (mg) is the resistance. The heavier something is, the more force and therefore more energy is required to move it up 1 m. Now, if we turn this how many turns of the crank instead of height, we are talking current and power (disregard this last sentence if it's confusing).

Power is always directly proportional to the resistance, because the voltage depends on the resistance. If you double the resistance, you will double the voltage. Since it's V^2 / R, notice the top of the equation goes up by 4, whereas the bottom goes up by 2, making an overall increase of 2.
 

The Brown Knight

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You have to decide which one of the two derived equations to use in the problem based on whether voltage V or current I is constant.

If V is constant and known, use P = V^2/R; e.g. if a battery is connected with the resistor in question and is providing a constant voltage V (this equation is particularly useful if the resistor is in parallel with other resistors and it's difficult/impossible to find the current going through it from the question)

If I is constant and known, use P = I^2R; e.g. if a battery is NOT connected with the resistor in question (this could happen in an RC circuit if a battery has initially charged a capacitor, and then the battery is removed and the capacitor is allowed to discharge)

Many times you can correctly use either one if you're given both the current through and voltage drop across the resistor (here you can best use P = IV)

Point is ask yourself: is the voltage/current changing or constant with the resistor? is the current/voltage known?
 
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