Express the power dissipated in a 100 Ω resistor in dB relative to 1 mW, when the voltage across the resistor is 1.0 V_rms

The voltage across the resistor = 1 V_rms

Resistance Value = 100 Ω

The power dissipated by the resistor is given by:

\(P = \frac{V_{rms}^2}{R}\)

\(P = \frac{1^2}{100}=\frac{1}{100}=10^{-2}~W\)

We are asked to evaluate the power dissipated with respect to 1 mW reference power.

\(P=\frac{10^{-2}}{10^{-3}}=10\)

In dB, this is expressed as:

\(P_{dB}=10~log_{10}(P)=10~log_{10}\frac{10^{-2}}{10^{-3}}\)

P_dB = 10 log₁₀(10) = 10 dB