Please have a look on this document. My question is about the text in maroon on page #3 where it says, "The cutoff frequency fc is the frequency above or below which the power of the circuit, which is most often a filter, is ½ the input power...".

At the critical frequency output voltage is 70.7% of the input voltage in a RC filter. What does it mean where the text says, "The cutoff frequency fc is the frequency above or below which the power of the circuit, which is most often a filter, is ½ the input power." Does it mean that at the critical frequency output power is half of input power in a RC circuit? I assume this is the case. Then, it says, "Since P = V^2/R, half the power is proportional to sqrt(1/2) the voltage." How is power proportional to sqrt(1/2) the input voltage?

Please help me. Thank you.

Regards

PG