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P5.26. Write an expression for the sinusoid shown in Figure P5.26 O of the form v(t) = Vm cos(wt + 0), giving the numerical values of Vm, w, and 0. Also, determine the phasor and the rms value of v(t). v(1) -1 -2 -3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0625 s - 1 (s)

P5.26. Write an expression for the sinusoid shown in Figure P5.26 O of the form v(t) = Vm cos(wt + 0), giving the numerical values of Vm, w, and 0. Also, determine the phasor and the rms value of v(t). v(1) -1 -2 -3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0625 s - 1 (s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**P5.26.** Write an expression for the sinusoid shown in Figure P5.26 of the form \[ v(t) = V_m \cos(\omega t + \theta) \] giving the numerical values of \( V_m \), \( \omega \), and \( \theta \). Also, determine the phasor and the rms value of \( v(t) \). --- **Explanation of the Graph in Figure P5.26:** The graph illustrates a sinusoidal waveform, which is a plot of \( v(t) \) versus time \( t \). - **Y-Axis (Voltage, \( v(t) \)):** Ranges from -3V to 3V, suggesting that the amplitude (\( V_m \)) of the waveform is approximately 3 volts. - **X-Axis (Time, \( t \)):** Marks values from 0 to 1 seconds, with clear labeling of a period around 0.0625 seconds. This indicates the time it takes for one complete cycle of the waveform. - **Wave Characteristics:** - **Peak Voltage (\( V_m \)):** The peak value of the sinusoid, determined visually from the graph, is about 3 volts. - **Period (T):** The complete cycle occurs approximately every 0.25 seconds, based on extrapolation from the labeled subdivisions (each labeled division is 0.0625 seconds). - **Angular Frequency (\( \omega \)):** Calculated using \( \omega = \frac{2\pi}{T} \) where \( T \approx 0.25 \) seconds. - **Phase Angle (\( \theta \)):** As the waveform appears to start from a peak, \( \theta \) might be zero or negligible for a cosine function starting at a maximum. - **RMS Value:** The root mean square value can be calculated as \( \text{RMS} = \frac{V_m}{\sqrt{2}} \). This graph represents the time-dependent behavior of the sinusoidal signal \( v(t) \).
Transcribed Image Text:**P5.26.** Write an expression for the sinusoid shown in Figure P5.26 of the form \[ v(t) = V_m \cos(\omega t + \theta) \] giving the numerical values of \( V_m \), \( \omega \), and \( \theta \). Also, determine the phasor and the rms value of \( v(t) \). --- **Explanation of the Graph in Figure P5.26:** The graph illustrates a sinusoidal waveform, which is a plot of \( v(t) \) versus time \( t \). - **Y-Axis (Voltage, \( v(t) \)):** Ranges from -3V to 3V, suggesting that the amplitude (\( V_m \)) of the waveform is approximately 3 volts. - **X-Axis (Time, \( t \)):** Marks values from 0 to 1 seconds, with clear labeling of a period around 0.0625 seconds. This indicates the time it takes for one complete cycle of the waveform. - **Wave Characteristics:** - **Peak Voltage (\( V_m \)):** The peak value of the sinusoid, determined visually from the graph, is about 3 volts. - **Period (T):** The complete cycle occurs approximately every 0.25 seconds, based on extrapolation from the labeled subdivisions (each labeled division is 0.0625 seconds). - **Angular Frequency (\( \omega \)):** Calculated using \( \omega = \frac{2\pi}{T} \) where \( T \approx 0.25 \) seconds. - **Phase Angle (\( \theta \)):** As the waveform appears to start from a peak, \( \theta \) might be zero or negligible for a cosine function starting at a maximum. - **RMS Value:** The root mean square value can be calculated as \( \text{RMS} = \frac{V_m}{\sqrt{2}} \). This graph represents the time-dependent behavior of the sinusoidal signal \( v(t) \).
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