Final answer:
The average value of a full-wave rectified voltage sinusoid is given by the expression Vavg = (2/π)Vo. For power calculations, the average power in an AC circuit is Pave = IrmsVrms, where Irms and Vrms represent the root mean square values of current and voltage, respectively.
Step-by-step explanation:
The mathematical expression for the average value of a rectified voltage sinusoid is related to the root mean square (rms) value of the voltage. An AC voltage that fluctuates sinusoidally with time is represented by V = Vo sin(2πft), where V is the voltage at time t, Vo is the peak voltage, and f is the frequency in hertz. For a full-wave rectified sinusoid, the average value, commonly known as the DC equivalent value, is Vavg = (2/π) Vo. However, for power calculations in AC circuits, the formula Pave = IrmsVrms is used, where Irms is the rms current and Vrms is the rms voltage, and rms stands for root mean square.
When considering the power associated with a sinusoidal wave, the average power expression is calculated by considering the impedance of the circuit and the rms voltage according to equation Pave = Irms^2R, where R is the resistance. The rms voltage itself is the peak voltage Vo multiplied by 1/√2.