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When dealing with alternating current (AC), it's important to consider the Root Mean Square (RMS) value rather than the peak value. This is because RMS values provide a more useful representation of the current's ability to do work, much like the way a DC equivalent would. The RMS current is calculated using the formula:\[I_{rms} = \frac{I_{peak}}{\sqrt{2}}\]This formula results from the statistical means by which AC current varies sinusoidally through time. Because it averages out the varying values over each cycle, it tells us the effective current that truly represents the power-delivering capability of an AC circuit. By using the peak current value of 2.5 A, the calculation yields an RMS current of approximately 1.77 A.

Similar to the RMS current, the Root Mean Square (RMS) voltage signifies the effective voltage in an AC circuit. RMS voltage gives a realistic measure of the AC voltage by equating its power-providing capacity to an equivalent DC voltage. The RMS voltage is calculated with:\[V_{rms} = \frac{V_{peak}}{\sqrt{2}}\]Here, the peak voltage value of 16 V is divided by \(\sqrt{2}\), providing an RMS voltage value of approximately 11.31 V. This value is practical for understanding and comparing the power dynamics in AC circuits, ensuring we account for how voltage swings periodically.

The average power output in an AC circuit is vital for determining how much power the circuit can deliver. The formula for average power output is:\[P_{avg} = I_{rms} \times V_{rms}\]Inserting the previously calculated RMS current and voltage values gives us:\[P_{avg} = 1.77 \, \text{A} \times 11.31 \, \text{V} \approx 20.02 \, \text{W}\]This calculation allows us to find the real power dissipated by the circuit. This power, measured in watts, is what's truly harnessed and used, lending insightful understanding into its efficiency and performance.

The concept of effective resistance is derived from Ohm's Law, where resistance is the ratio of voltage to current. In AC circuits, we use RMS values to calculate effective resistance, ensuring that the measurements are realistic and consistent with real-world conditions. The formula applied is:\[R = \frac{V_{rms}}{I_{rms}}\]By using our RMS voltage of 11.31 V and RMS current of 1.77 A, we find the effective resistance to be approximately 6.39 Ω. Understanding effective resistance provides insight into the opposition a circuit offers to the flow of current, which is crucial for designing efficient circuits and ensuring safe operation.