1. STEM Application Electric Circuits
Andy Escobedo
Math1275
STEM Application Electric Circuits

2. Electric AC Circuits
The STEM Application I choose was Electric Circuit and the reason for this is because I'm majoring in electrical engineering technology. The interpretation for circuits all relies on Ohm’s laws where current = voltage/resistance , voltage = current*resistance and resistance = current/voltage.
I would be working on Alternating Current circuits (AC) where “the voltage across a resistance is in phase with the current by 90°, the voltage across a capacitor lags the current by 90°, and the voltage across an inductance leads the current by 90°”

3. Representing Voltage using complex plane
Utilizing a complex plane would give us a better idea to comprehend the resistors, capacitors, and inductors. Considering that the voltage is across the resistor, inductor, and capacitor. Resistors would be on “the horizontal axis as its consider as a real quantity.” The inductor would be in “the positive vertical axis as its consider as a positive imaginary quantity.” The capacitor would be in “the negative vertical axis as its consider as a negative imaginary quantity.”

4. A particular AC circuit has a resistor of 8Ω, a reactance across an inductor of 10Ω and a reactance a across a capacitor of 12Ω. Express the impedance of the circuit as a complex number in polar form.

5. In this case ,we have XL – XC = 10 – 12 = –2Ω
|z| = |a+bi|
z^2 = a^2+b^2
(Pythagorean Theorem)
|z| = sqrt(8^2+2^2)
Z = sqrt(68)=8.246

6. Now to express it in polar form.
Utilizing a calculator I found the degree angle which is °, in addition, I also found z by using the Pythagorean Theorem.
The way I obtain the angle is utilizing the trig function of tan which is tan(x)=opp/adj, however, I'm looking for the angle, not the side so I use the inverse of tan which is tan^-1(opp/adj). So moreover z = magnitude angle is °Ω

7. Sources
matic.com/watch/cbnQf06h1i