Minimum resistance to prevent overheating in AC circuit

[songoku]

Homework Statement

An alternating current supply is connected in series with a resistor R. The variation with time t (measured in seconds) of the current I (measured in amps) in the resistor is given by the expression I = 9.9 sin(380t). To prevent over-heating, the mean power dissipated in resistor R must not exceed 400 W. Calculate the minimum resistance of R

Relevant Equations

mean power = $I_{rms}^2 \times R$

My calculation: $400=\left(\frac{9.9}{\sqrt{2}}\right)^2 R$ and I got R = 8.2 ohm

But the answer key used I_o (9.9 A) instead of I_rms

Why?

Thanks

 

[Steve4Physics]

You are correct(8.2Ω). It's a mistake in the 'answer key' - it sometimes happens.

 

[scottdave]

It would only be speculation on my part as to "why" they did not use RMS current. Books make mistakes sometimes. Did you ask your instructor about it? Does the book publisher have a website for errata?

 

[songoku]

It would only be speculation on my part as to "why" they did not use RMS current. Books make mistakes sometimes. Did you ask your instructor about it? Does the book publisher have a website for errata?

I haven't asked him, I just did the practice myself. The question is not from book, it is given by the teacher and on the last page there is working and answer to help the students.

Thank you very much for the help Steve4Physics and scottdave