1. Given the following sine wave equation: v(t) = 40 sin (440) V a) Find the Pea

Question

1. Given the following sine wave equation: v(t) = 40 sin (440) V a) Find the Peak Voltage (Vp). b) Find the Peak-to-Peak Voltage (Vp.p). c) Find the RMS Voltage (V). d) Find the Average Voltage (Vay) e) Find the Angular Frequency () f Find the electrical frequency (0) g) Find the period (T). 2. Given the following electrical circuit below: a) Find the impedance (Z) in polar form and rectangular form. b) Find the current in polar form and rectangular form. c) Plot the voltage, current, and impedance in polar form in the complex plane.

Explanation / Answer

1)

V = 400 * sin(440 t)

V = Vm * sin(440 * t)

a) peak voltage = Vm

peak voltage = 400 V

b)

peak to peak voltage = 2 * Vpeak

peak to peak voltage = 2 * 400

peak to peak voltage = 800 V

c)

RMS voltage = Vpeak/sqrt(2)

RMS voltage = 400/sqrt(2)

RMS voltage = 282.8 V

d)

average voltage = 2*Vpeak/pi

average voltage = 2 * 400/pi

average voltage = 254 V

e)

angular frequency, w = 440 rad/s

f) frequency = w/2pi

frequency = 440/(2pi)

frequency = 70 Hz
g)
period = 1/frequency

period = 1/70

period = 0.0143 s

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