4) Power is being supplier to an industrial site. The current into building 1 is i, = 100 cos(120nt + Amps. The current into building 2, which has a large solar farm on the roof, is i, = 3n 300 cos ( 120nt + ") Amps. a. What frequency in Hz is being provided? b. The current iline in the line that feeds both the two buildings must be the sum of the two currents. What is this current? с. What is the time shift of this current? d. By hand, sketch a plot of all three currents. Be sure to label it so that the three different amplitudes and 3 different phase angles are clear. e. Using a software tool, confirm your work to this point and reproduce your plot. f. A third building is being added to the site. If it needs 200 Amps of current at the same frequency and is added to the same line, what phase angle for building 3 would allow the current in the power line (the sum) to have a phase angle as close to t as possible? (another way of saying this is that you want to reduce the imaginary part of the sum of the building currents by as much as possible.)
4) Power is being supplier to an industrial site. The current into building 1 is i, = 100 cos(120nt + Amps. The current into building 2, which has a large solar farm on the roof, is i, = 3n 300 cos ( 120nt + ") Amps. a. What frequency in Hz is being provided? b. The current iline in the line that feeds both the two buildings must be the sum of the two currents. What is this current? с. What is the time shift of this current? d. By hand, sketch a plot of all three currents. Be sure to label it so that the three different amplitudes and 3 different phase angles are clear. e. Using a software tool, confirm your work to this point and reproduce your plot. f. A third building is being added to the site. If it needs 200 Amps of current at the same frequency and is added to the same line, what phase angle for building 3 would allow the current in the power line (the sum) to have a phase angle as close to t as possible? (another way of saying this is that you want to reduce the imaginary part of the sum of the building currents by as much as possible.)
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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See attached P4
![**Problem 4: Power Supply to an Industrial Site**
Power is being supplied to an industrial site. The current into building 1 is given by:
\[ i_1 = 100 \cos \left(120 \pi t + \frac{\pi}{4}\right) \, \text{Amps} \]
The current into building 2, which has a large solar farm on the roof, is:
\[ i_2 = 300 \cos \left(120 \pi t + \frac{3\pi}{4}\right) \, \text{Amps} \]
**Questions:**
a. **What is the frequency in Hz being provided?**
b. **The current \( i_{\text{line}} \) in the line that feeds both the two buildings must be the sum of the two currents. What is this current?**
c. **What is the time shift of this current?**
d. **By hand, sketch a plot of all three currents. Be sure to label it so that the three different amplitudes and three different phase angles are clear.**
e. **Using a software tool, confirm your work to this point and reproduce your plot.**
f. **A third building is being added to the site. If it needs 200 Amps of current at the same frequency and is added to the same line, what phase angle for building 3 would allow the current in the power line (the sum) to have a phase angle as close to \(\pi\) as possible? (Another way of saying this is that you want to reduce the imaginary part of the sum of the building currents by as much as possible.)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ce7fe7-6055-4d88-a2fe-fb962619b6d1%2F178d0604-231c-46b4-be2d-47eeab55e25e%2Fmjpji6n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4: Power Supply to an Industrial Site**
Power is being supplied to an industrial site. The current into building 1 is given by:
\[ i_1 = 100 \cos \left(120 \pi t + \frac{\pi}{4}\right) \, \text{Amps} \]
The current into building 2, which has a large solar farm on the roof, is:
\[ i_2 = 300 \cos \left(120 \pi t + \frac{3\pi}{4}\right) \, \text{Amps} \]
**Questions:**
a. **What is the frequency in Hz being provided?**
b. **The current \( i_{\text{line}} \) in the line that feeds both the two buildings must be the sum of the two currents. What is this current?**
c. **What is the time shift of this current?**
d. **By hand, sketch a plot of all three currents. Be sure to label it so that the three different amplitudes and three different phase angles are clear.**
e. **Using a software tool, confirm your work to this point and reproduce your plot.**
f. **A third building is being added to the site. If it needs 200 Amps of current at the same frequency and is added to the same line, what phase angle for building 3 would allow the current in the power line (the sum) to have a phase angle as close to \(\pi\) as possible? (Another way of saying this is that you want to reduce the imaginary part of the sum of the building currents by as much as possible.)**
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