University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2021
Views:

119

Pages:

6
Author:

Athena Harrison

Tuesday 5/7/2013 LCL EUL: v(t) + e(t)R + L di(t)/dt = 0 -> 1st order differential equation v(t) = Vm cos(wt) Linear CKT v(t) = Re{V(t)} = Vm cos(wt+θ) Variables: Linear CKT means that both input and output current have the same form. v(t) = Re{V(t)} = Real part of v(t) = Vmcos(wt+θ) Plug in 1: Ri(t) + L di/dt = v(t) RIm e^(jwt+θ) + LImjwe^(jwt+θ) = Vme^(jwt+θ) RIm + jwlIm = Vm Im(R+jwl) = Vm Rectangular: Im = Vm / √(R² + w²L²) θ = -tan⁻¹(wL/R) Polar: Im = Vm∠-θ i(t) = Im cos(wt+θ) I = Im∠θ From ② & ③: I = Vm / √(R² + ω²L²) ∠θ - tan⁻¹(ωL/R) i(t) = Vm / √(R² + ω²L²) cos(ωt + θ - tan⁻¹(ωL/R)) Time Domain Phasor: i(t) = Im cos(ωt + φ) ⇔ I = Im∠φ ≡ Im e^(jφ) ≡ Im cosφ + jIm sinφ ex: a) v₁(t) = 12 cos(200t - 35°) v₂(t) = -12 cos(200t - 35°) Find V₁ & V₂: V₁ = 12∠-35° V₂ = -12∠-35° = 12∠-35° + 180° = 12∠145° The (-) sign means a phase shift by 180°. b) i₂(t) = 10 sin(12t + 30°), find I₂? First, we have to transform sine to cosine: i₂(t) = 10 cos(12t + 30° - 90°) = 10 cos(12t - 60°) I₂ = 10∠-60° Negative frequency means rotating clockwise! 1) Resistor: v(t) = i(t).R v(t) = Vm cos(ωt + θ) i(t) = Im cos(ωt + φ) V = IR Vm∠θ = ImR∠φ * Generalized Ohm's law: V = I*Z Impedance [Ω] Y = 1/Z Admittance [1/Ω] = mho 7/2/2013