Question

Write the complex sinusoidal waveform expression from this data: Voltage Vₚₖ 20, Frequency Hz 2000, Phase (Rad) -π.

A. V(t) = 20 sin(4000pi t - pi)
B. V(t) = 20 cos(4000pi t - pi)
C. V(t) = 20 sin(2000pi t - pi)
D. V(t) = 20 cos(2000pi t - pi)

Answer 1

The correct expression for the complex sinusoidal waveform given the amplitude of 20 V, the frequency of 2000 Hz, and phase of -π radians is V(t) = 20 sin(4000πt - π), corresponding to option A.

Step-by-step explanation:

The complex sinusoidal waveform expression from the given data can be characterized by its amplitude (Vₚₖ), which is the peak voltage, its frequency (in Hertz), and its phase (in radians). According to the data provided:

• Amplitude (Vₚₖ): 20 V
• Frequency (f): 2000 Hz
• Phase (ϕ): -π radians

Using the formula for a sinusoidal wave, V(t) = Vₚₖ sin(2πft + ϕ), and substituting the given values, we get:

V(t) = 20 sin(2π(2000)t - π)

This simplifies to:

V(t) = 20 sin(4000πt - π)

Among the options provided:

1. V(t) = 20 sin(4000πt - π) (Correct)
2. V(t) = 20 cos(4000πt - π)
3. V(t) = 20 sin(2000πt - π)
4. V(t) = 20 cos(2000πt - π)

The correct expression for the complex sinusoidal waveform is V(t) = 20 sin(4000πt - π), which matches option A.