Understanding the V(in)=V(max).sin(wt) Formula for DC Smoothing Circuits

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The formula V(in) = V(max) * sin(wt) describes a time-varying voltage in a DC smoothing circuit, where V(in) represents the instantaneous voltage, V(max) is the peak voltage, and sin(wt) indicates the sinusoidal nature of the waveform. The angular frequency w, measured in radians per second, determines how quickly the waveform oscillates, with the cycle frequency f being related to w by the equation f = 2*pi*w. This formula is crucial for calculating the time at which the waveform reaches a specific minimum voltage, V(min). Understanding these components is essential for analyzing the behavior of DC smoothing circuits in power supply applications. The discussion highlights the importance of grasping the relationship between these variables for effective circuit design.
Sparkyian
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Can someone please explain to me in brief detail as to what each expression means for the given formula:-

V(in)=V(max).sin(wt)

and to how this formula works? It is a formula that has been given to me in order to work out time at which a waveform=V(min) for a dc smoothing circuit with a typical power supply.
 
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V(in) is a voltage that changes with time. It changes with time in a sinusoidal fashion, with an amplitude of V(max). The angular frequency is w (units: radians/second) or a cycle frequency f=2*pi*w (units: cycles/second or Hz).
 
Thank you very much, I now understand.
 

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