A sinusoidal voltage v(t) = 150 sin(1000xt + 45°) is depicted in Fig. 1. Evaluate the time ti when the sinusoid crosses the t-axis (Hint: a standard representation of a sinusoid is a(t) = Am sin(27 ft + ¢)), where Am is the amplitude, ƒ is the cyclic frequency, and ø is the phase. Moreover, the period, T, can be calculated as T = 1/f. 200 v(t) 100 -100 v = 0 -200 tị T 37 t Figure 1: Figure for Question 1 (a) Mathematically show that the integral of v(t) is transformed to the phasor domain as V/jw, such that V dt jw' where v(t) = Vm cos(wt + ø) = Re(Vmei (wt+ø)) = Re(Vejwt) and V = Vmej®.

A sinusoidal voltage v(t) = 150 sin(1000xt + 45°) is depicted in Fig. 1. Evaluate the time ti when the sinusoid crosses the t-axis (Hint: a standard representation of a sinusoid is a(t) = Am sin(27 ft + ¢)), where Am is the amplitude, ƒ is the cyclic frequency, and ø is the phase. Moreover, the period, T, can be calculated as T = 1/f. 200 v(t) 100 -100 v = 0 -200 tị T 37 t Figure 1: Figure for Question 1 (a) Mathematically show that the integral of v(t) is transformed to the phasor domain as V/jw, such that V dt jw' where v(t) = Vm cos(wt + ø) = Re(Vmei (wt+ø)) = Re(Vejwt) and V = Vmej®.

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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