Electric Power - Which formula to use and when?

[MeAndMyLucidLife]

Homework Statement

:
[/B]
If the length of the filament of a heater is reduced by 10%, the power of the heater:
Options are-
a) increases by about 9%.
b) increases by about 11%.
c) increases by about 19%.
d) decreases by about 10%.

Homework Equations

:

P[/B]=I²R
Or
P=V²/R

Where P=power; I=current; V=potential difference; R=resistance.

The Attempt at a Solution

:[/B]
The answer given to this problem is: b) increases by about 11%.

If we solve this question using the formula P=V²/R, we get the correct answer.
But(obviously), we get the wrong answer when we use P=I²R.

However, I am totally confused about which formula of Power to use, and in which situations?

As one formula is used when V is kept constant, while the other one is used when I is kept constant.
Also, in one formula, R is directly proportional to power, while in the latter, it is inversely proportional!

What should be the thought process before choosing which formula to use when?

Please Help!
Thank You

 

[stockzahn]

P=I²R
Or
P=V²/R

Imagine you plug in a different heater with more power: Do you think the different heater will change the voltage of the grid or just consumes a different amount of current?

 

[gneill]

Household electricity is provided at a fixed voltage. Appliances draw whatever current they need, so the current is variable.

In your situation you're changing the appliance's resistance so that the current it draws will change. Does that help?

 

[PKM]

However, I am totally confused about which formula of Power to use, and in which situations?

Just note which one between $I$ & $V$ is independent of $R$ for the case in hand. The voltage supply $V$ remains the same for an electric heater, and current is subject to change with resistance, so you need to apply the second formula.

 

[PKM]

Also, in one formula, R is directly proportional to power, while in the latter, it is inversely proportional!

Why should they not be? Is considering once $I$ as constant, and another time $V$ as constant, (when $R$ is variable) the same? Are they not related by $R$ itself?

 

[MeAndMyLucidLife]

Household electricity is provided at a fixed voltage. Appliances draw whatever current they need, so the current is variable.

In your situation you're changing the appliance's resistance so that the current it draws will change. Does that help?

Yes!
So in this problem, it was an understood fact that voltage remains constant.
Thanks a lot!

 

[MeAndMyLucidLife]

Why should they not be? Is considering once $I$ as constant, and another time $V$ as constant, (when $R$ is variable) the same? Are they not related by $R$ itself?

Ya...Got It!
V=IR
All V, I, and R are mutually dependent.
Keeping one of them constant gives us the relation between the other two.
Thanks a lot