What is the average power if the resistance R is doubled in an AC circuit?

[Coop]

Homework Statement

The average power dissipated by a resistor is 4.0 W. What is the average power if the resistance R is doubled?

Homework Equations

$$P_{rms}=I_{rms}^2R=I_{rms}V_{rms}=\frac{V_{rms}^2}{R}$$

The Attempt at a Solution

I am told the answer is 2.0 W. But here's what I am confused about...it is valid to use all of the power equations above for this problem, correct? Well if I use

$$P_{rms}=I_{rms}^2R$$ I get the new average power to be 8.0 W.

But if I use the

$$P_{rms}=\frac{V_{rms}^2}{R}$$ I get the new average power to be 2.0 W.

How do I know which equation to use?

Thanks.

 

[dauto]

The problem assumes the applied voltage is the same. You should always assume that unless otherwise stated because most power sources produce constant voltage and variable current (assuming you didn't do something crazy such as a short-circuit). So, when you replace a resistor with a different resistor, the current changes but the applied voltage doesn't, hence the second equation gives the correct answer.

 

[Coop]

The problem assumes the applied voltage is the same. You should always assume that unless otherwise stated because most power sources produce constant voltage and variable current (assuming you didn't do something crazy such as a short-circuit). So, when you replace a resistor with a different resistor, the current changes but the applied voltage doesn't, hence the second equation gives the correct answer.

So I can't use I^2R, because by definition the current would also be a different value for a new R? But we know the voltage will stay the same for a new R, so we can use V^2/R?

 

[Coop]

Thanks :)

 

[HalfLostAndSearching]

I would suggest using the equation that is most appropriate for the given situation. In this case, since the resistance is being doubled in an AC circuit, it is more appropriate to use the equation P_{rms}=\frac{V_{rms}^2}{R}. This equation takes into account the change in resistance and gives a more accurate representation of the average power in the circuit.

It is also important to note that the power equations you have listed are for an AC circuit, where the current and voltage are constantly changing. In an AC circuit, the average power is calculated using the root mean square (rms) values of current and voltage, which take into account the changing values.

In summary, it is important to choose the appropriate equation for the given situation and to use the correct values (such as rms values for an AC circuit) in order to get an accurate result.