Resistive dissipation and Ohm's law

[AdrianMachin]

Homework Statement

A potential difference V is connected across a device with resistance R, causing current i through the device. Rank the following variations according to the change in the rate at which electrical energy is converted to thermal energy due to the resistance, greatest change first:
(a) V is doubled with R unchanged,
(b) i is doubled with R unchanged,
(c) R is doubled with V unchanged,
(d) R is doubled with i unchanged.

Homework Equations

$$P= {i^2} R$$
$$P= \frac {V^2} R$$

The Attempt at a Solution

I know and understand that (a) and (b) result in $P'=4P$, but I'm not sure if I judge (c) and (d) variations correctly. I guess that the answer to (c) and (d) is that there would be no change if the device obeys Ohm's law.

 

[cnh1995]

You can assume some values for V and R and check each condition. You have listed the correct equations.

guess that the answer to (c) and (d) is that there would be no change if the device obeys Ohm's law.

No change in what?

 

[AdrianMachin]

You can assume some values for V and R and check each condition. You have listed the correct equations.

No change in what?

No change in $P$.

 

[cnh1995]

No change in $P$.

There will be changes in P according to the equations you've listed.

 

[AdrianMachin]

There will be changes in P according to the equations you've listed.

I think I was wrong to worry about the Ohm's law, it is actually embedded in those two equations.

 

[scottdave]

It looks like they only want you to worry about the changes that each choice asks about. Obviously if R is kept constant (in the first two), then a change in V results in a change in I, as well as a change in I would result in a change in V (per Ohm's Law). So the bottom two tell you that somehow the device has changed (maybe it is a potentiometer, which you can adjust), and they are able to configure the supply to remain constant in the listed variable.