Math Problem Statement
Given values
I_R = 4 # purely real (in A) I_L_magnitude = 7 # in A I_L_phase_deg = 70 # in degrees I_C_magnitude = 7.23 # in A I_C_phase_deg = -90 # in degrees
Convert phase angles to radians
I_L_phase_rad = math.radians(I_L_phase_deg) I_C_phase_rad = math.radians(I_C_phase_deg)
Convert currents into their complex forms (phasors)
I_L = cmath.rect(I_L_magnitude, I_L_phase_rad) I_C = cmath.rect(I_C_magnitude, I_C_phase_rad)
I_R is purely real, so it's just 4
I_R_complex = complex(I_R, 0)
Calculate the total current (phasor sum)
I_total = I_R_complex + I_L + I_C
Get magnitude and phase of the total current
I_total_magnitude = abs(I_total) I_total_phase_deg = math.degrees(cmath.phase(I_total))
I_total_magnitude, I_total_phase_deg
Solution
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Math Problem Analysis
Mathematical Concepts
Phasor Analysis
Complex Numbers
AC Circuits
Formulas
Conversion of phase angles: radians = degrees * (π / 180)
Complex form of phasors: I = magnitude * (cos(phase) + j*sin(phase))
Phasor sum: I_total = I_R + I_L + I_C
Magnitude of a complex number: |I_total| = sqrt(real^2 + imag^2)
Phase of a complex number: phase = atan2(imag, real)
Theorems
Phasor Addition Theorem
Suitable Grade Level
Undergraduate Electrical Engineering
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