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!
KVL and KCL
KVL stands for Kirchhoff voltage law. KVL states that the total voltage drops around the loop in any closed electric circuit is equal to the sum of total voltage drop in the same closed loop.
Sign Convention
Science and technology incorporate some ideas and techniques of their own to understand a system skilfully and easily. These techniques are called conventions. For example: Sign conventions of mirrors are used to understand the phenomenon of reflection and refraction in an easier way.
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°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77635a5b-6f9a-44e3-8a78-e1773363d354%2F45e0003a-5fda-4cf2-9bcc-b4fd8bcbf8a0%2Fyllygnn_processed.png&w=3840&q=75)
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