Part 1: A linear electrical load draws 1₁ A at a 0.72 lagging power factor. See the table to find ½ for your student ID. When a capacitor is connected, the line current dropped to 122 A and the power factor improved to 0.98 lagging. Supply frequency is 50 Hz. a. Let the current drawn from the source before and after introduction of the capacitor be 1₁ and I₂ respectively. Take the source voltage as the reference and express 11 and 12 as vector quantities in polar form. b. Obtain the capacitor current, Ic = 12 − I₁, graphically as well as using complex number manipulation. Compare the results. c. Express the waveforms of the source current before (į (t)) and after (i2(t)) introduction of the capacitor in the form Im sin(2лft + 0). Hand sketch them on the same graph. Clearly label your plots. d. Analytically solve i̟2(t) − i₁ (t) using the theories of trigonometry to obtain the capacitor current in the form, ic(t) = Icm sin(2πft + 0c). Compare the result with the result in Part b.
Part 1: A linear electrical load draws 1₁ A at a 0.72 lagging power factor. See the table to find ½ for your student ID. When a capacitor is connected, the line current dropped to 122 A and the power factor improved to 0.98 lagging. Supply frequency is 50 Hz. a. Let the current drawn from the source before and after introduction of the capacitor be 1₁ and I₂ respectively. Take the source voltage as the reference and express 11 and 12 as vector quantities in polar form. b. Obtain the capacitor current, Ic = 12 − I₁, graphically as well as using complex number manipulation. Compare the results. c. Express the waveforms of the source current before (į (t)) and after (i2(t)) introduction of the capacitor in the form Im sin(2лft + 0). Hand sketch them on the same graph. Clearly label your plots. d. Analytically solve i̟2(t) − i₁ (t) using the theories of trigonometry to obtain the capacitor current in the form, ic(t) = Icm sin(2πft + 0c). Compare the result with the result in Part b.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text:Part 1:
A linear electrical load draws 1₁ A at a 0.72 lagging power factor. See the table to find ½ for your
student ID. When a capacitor is connected, the line current dropped to 122 A and the power factor
improved to 0.98 lagging. Supply frequency is 50 Hz.
a. Let the current drawn from the source before and after introduction of the capacitor be 1₁ and I₂
respectively. Take the source voltage as the reference and express 11 and 12 as vector
quantities in polar form.
b. Obtain the capacitor current, Ic = 12 − I₁, graphically as well as using complex number
manipulation. Compare the results.
c. Express the waveforms of the source current before (į (t)) and after (i2(t)) introduction of the
capacitor in the form Im sin(2лft + 0). Hand sketch them on the same graph. Clearly label your
plots.
d. Analytically solve i̟2(t) − i₁ (t) using the theories of trigonometry to obtain the capacitor current
in the form, ic(t) = Icm sin(2πft + 0c). Compare the result with the result in Part b.
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