I'm confused as to how they simplified the one portion of this and ended up with 10^6 = R^2 + 589.5^2  My calculations are removing the 10 from the numerator, then squaring to remove the root, leaving me with .00001= R^2 + 589.5^2   I cant seem to wrap my head around what im doing wrong to end up with a negative number instead of 10,000,000. Everything else makes sense to me. Been 20 years since algebra classes so it could just be that. Thanks in advance for the help!

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter7: Alternating Current, Power Distribution, And Voltage Systems
Section: Chapter Questions
Problem 7RQ
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I'm confused as to how they simplified the one portion of this and ended up with 10^6 = R^2 + 589.5^2 

My calculations are removing the 10 from the numerator, then squaring to remove the root, leaving me with .00001= R^2 + 589.5^2

 

I cant seem to wrap my head around what im doing wrong to end up with a negative number instead of 10,000,000. Everything else makes sense to me. Been 20 years since algebra classes so it could just be that. Thanks in advance for the help!

Explanation of Solution
Given:
The given circuit is:
10mA
10 V
f = 10 kHz
0.027μF
Calculation:
The reactance value of the capacitor can be calculated as
Хо
=
Xc =
2xFC
2*(10×10³) (0.027×10−5)
Хо = 589.5.2
The impedance of the circuit can be calculated as
Z = R-jXc
Z = R - j589.5
Z=√√R2+589.52 (tan-1589.5)
The current can be calculated by using the Ohm's law,
I = 1/
10 × 10-3
10
=
√R²+589.5²
R2589.52-
=
= 106
R² = 652489.75
R = 807.77.2
The value of the resulting angle will be
0 = tan-1 (589.5)
0 = tan
-1
589.5
0 = 36.12°
Transcribed Image Text:Explanation of Solution Given: The given circuit is: 10mA 10 V f = 10 kHz 0.027μF Calculation: The reactance value of the capacitor can be calculated as Хо = Xc = 2xFC 2*(10×10³) (0.027×10−5) Хо = 589.5.2 The impedance of the circuit can be calculated as Z = R-jXc Z = R - j589.5 Z=√√R2+589.52 (tan-1589.5) The current can be calculated by using the Ohm's law, I = 1/ 10 × 10-3 10 = √R²+589.5² R2589.52- = = 106 R² = 652489.75 R = 807.77.2 The value of the resulting angle will be 0 = tan-1 (589.5) 0 = tan -1 589.5 0 = 36.12°
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