Answer:
Z = 29.938Ω ∠22.04°
I = 2.494A
Explanation:
Impedance Z is defined as the total opposition to the flow of current in an AC circuit. In an R-L-C AC circuit, Impedance is expressed as shown:
Z² = R²+(Xl-Xc)²
Z = √R²+(Xl-Xc)²
R is the resistance = 4Ω
Xl is the inductive reactance = ωL
Xc is the capacitive reactance =
1/ωc
Given C = 12 μF, L = 6 mH and ω = 2000 rad/sec
Xl = 2000×6×10^-3
Xl = 12Ω
Xc = 1/2000×12×10^-6
Xc = 1/24000×10^-6
Xc = 1/0.024
Xc = 41.67Ω
Z = √4²+(12-41.67)²
Z = √16+880.31
Z = √896.31
Z = 29.938Ω (to 3dp)
θ = tan^-1(Xl-Xc)/R
θ = tan^-1(12-41.67)/12
θ = tan^-1(-29.67)/12
θ = tan^-1 -2.47
θ = -67.96°
θ = 90-67.96
θ = 22.04° (to 2dp)
To determine the current, we will use the relationship
V = IZ
I =V/Z
Given V = 12V
I = 29.93/12
I = 2.494A (3dp)
Answer: It is a nominal rate per year
