Question

Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively.​

Answer 1

Answer:

30 okokokokokokokokok

Answer 2

Step-by-step explanation:

When connected in series, the component impedances are added together

(1) Z=R+iw\cdot L+ \frac{1}{iw \cdot C}Z=R+iw⋅L+iw⋅C1

To determine the phase angle between voltage and current, impedance should be represented in the Euler's form

Z=|Z|\cdot e^{iarg(Z)}Z=∣Z∣⋅eiarg(Z)

Determine first real and imaginary parts of the impedance (1) Z=R+iXZ=R+iX . We can see reactanceX=Lw-\frac{1}{Cw}X=Lw−Cw1 . Thus

|Z|=\sqrt{R^2+X^2}=\sqrt{R^2+(Lw-1/Cw)^2}=\sqrt{30^2+(184-144)^2}=50\Omega∣Z∣=R2+X2=R2+(Lw−1/Cw)2=302+(184−144)2=50Ω

arg(Z)=arctan(\frac{X}{R})=arctan(\frac{Lw-\frac{1}{Cw}}{R})=arctan(\frac{40}{30})=53\degreearg(Z)=arctan(RX)=arctan(RLw−Cw1)=arctan(3040)=53°

Answer: The phase angle between voltage and current {\displaystyle \theta } =53\degreeθ=53°