the reletionship between the flow of electricity, i(capitalized), ina circut,the resistance to the flow,Z,call

Question

(cont.) -ed impedance, and the electromotive force, E, called voltage, is given by the formula E= I (times) Z. Electrical engineers use i to represent the imaginary unit. An electrical engineer is designing a circut that is to have a current of (6-i8)amps. If impedance of the circut is (14+i8) ohms, find the voltage.

Answer 1

E = (6 - 8i) * (14 + 8i) = 84 + 48i - 112i + 64 = 148 - 64i
i represents the reactance of the circuit, in this case it is mostly capacitive, because it's negative.

Answer 2

V=IZ

=(6-j8)(14+j8)

= 84+j48-112j+64

=148-j64

which if I could remember Tan Imag/real?
I would not have to convert to Polar at all

but as I can't (let the calculator do the work for too long lol)

in Polar it's 161.245 Angle -23.385


So I challenge the "top contributor" ...you do NOT have to convert to polar at all


the other answer "mostly capacitance" ....since when has -23 degrees been close to -90 degrees?

Answer 3

E=IZ
=(6-j8)*(14+j8)

in polar form,
magnitude of I=√(6^2+(-8)^2)=10
angle of I= inverse tangent ( (-8)/6)=(-53.13)º

magnitude of Z=√(14^2+8^2)=16.12
angle of Z= inverse tangent (8/14)=29.74º

So,
magnitude of E=(10*16.12)=161.2
angle of E=(-53.13+29.74)=(-23.39)º

In rectangular form,
E=161.2*( sine(-23.39º)+j*cosine(-23.39º) )
=148-j64

You can do this by any scientific to calculate 'complex number' in any format (either Polar or Rectangular)

Answer 4

To multiply 2 complex numbers, (6 - 8i) * (14 + 8i), you need to convert them to polar form. Then, you multiply the radii (magnitudes) and add the phase angles to get the resultant complex voltage.

6 - 8i = magnitude: 10, phase angle: 306.86 degrees (-53.14)
14 + 8i = magnitude: 16.12, phase: 29.74 degrees

Result: 161.2 volts, phase -23.4 degrees.
148 - 64.0i Volts

.