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Completely wrong. V=√(P*R)V=P^2/(2*R)
Considering that the source impedance is outside the circuit of interest, I vote for V=sqrt(P*R).Should the V=sqrt(2*P*R) or V=sqrt(P*R) here?
If -20 dBm is the input level at the antenna of impedance 50 ohms, and if its matched, then you only get -23 dBm at your load
You seem to be confused with the concept of matched sources. There is no such power loss in the antenna.