Electrical Circuits - Equations

Question 1

v(t) = vpsin(wt+φ)
v(t) = vpexp(j(wt+φ))

Answer 1

vp = peak value
w = angular frequency 2pif (rad/s)
f = frequency (Hz)
φ = phase angle (rad)

Question 2

Xᶫ =

Answer 2

Xᶫ = v/i = jwL

Question 3

parallel impedances equation

Answer 3

Z = Z₁Z₂/(Z₁+Z₂)

Question 4

current equation for unloaded potential divider: i =

Answer 4

i = vᵢ / (Z₁+ Z₂)

Question 5

Current division equations: v = and i₁ =

Answer 5

v = iZ₁Z₂/(Z₁+Z₂)
i₁ = v/Z₁ = iZ₂/(Z₁+Z₂)

Question 6

Power dissipated in AC circuit, P = (Watts)

Answer 6

P = 0.5(iₚvₚ)cos(φ)
cos(φ) is power factor

Question 7

Transformers:
Turns ratio, n =
primary impedance, Zₚ =

Answer 7

n = Nₚ/Nₛ
Zₚ = vₚ/iₚ = n²Zₛ

Question 8

Maximum power transfer to load:
when Rᶫ = Rt and iₚ = vt/ 2Rt

Answer 8

Pmax = 0.5(iₚ)²Rᶫ

Question 9

Conjugate matching: load impedance = complex conjugate of thevenin impedance for max power transfer

Answer 9

Zᶫ = Zt*

Question 10

Source Current in Norton’s theorem

Answer 10

Iₛ = V/Z