Problem # 5Consider the sinusoidal voltage and current shown below:v(t) = 170 cos(120zt - 60°) V and i(t) = 60 sin(120xt - 30°) A.Plot v(t) and i(t) and determine if the current is leading or lagging the voltage.Find the Phasor representations of both voltage and current.Determine the rms values of both voltage and current.Determine the apparent power, S, P, Q, pf, and r.f.a)b)c)d)

Answered: Problem # 5 Consider the sinusoidal…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Problem # 5
Consider the sinusoidal voltage and current shown below:
v(t) = 170 cos(120zt - 60°) V and i(t) = 60 sin(120xt - 30°) A.
Plot v(t) and i(t) and determine if the current is leading or lagging the voltage.
Find the Phasor representations of both voltage and current.
Determine the rms values of both voltage and current.
Determine the apparent power, S, P, Q, pf, and r.f.
a)
b)
c)
d)

Expert Solution

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According to question:

The expression of voltage in sine form is written as

$∵ v (t) = 170 \cos \{120 π t - 60^{0}\} \Rightarrow v (t) = 170 \sin \{90^{0} + 120 π t - 60^{0}\} \Rightarrow v (t) = 170 \sin \{120 π t + 30^{0}\} V$

The plot of v(t) for time interval -0.02<t<0.02 is drawn as

The plot of i(t) for time interval -0.02<t<0.02 is drawn as

Now checking whether current is lagging or leading is given below:

$∵ v (t) = 170 \sin [120 π t + 30^{0}] V \Rightarrow ϕ_{v} = 30^{0} ∵ i (t) = 60 \sin [120 π t - 30^{0}] A \Rightarrow ϕ_{i} = - 30^{0} ∵ ϕ_{v} - ϕ_{i} = 30^{0} - (30^{0}) \Rightarrow ϕ_{v} - ϕ_{i} = 60^{0} \Rightarrow i (t) lags v (t) by 60^{0} .$