Question

Fine the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 ohms, 144 ohms and 30 ohms respectively. Also calculate the phase angle between voltage and current

Answer 1

When connected in series, the component impedances are added together

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

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

$Z=|Z|\cdot e^{iarg(Z)}$

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

$|Z|=\sqrt{R^2+X^2}=\sqrt{R^2+(Lw-1/Cw)^2}=\sqrt{30^2+(184-144)^2}=50\Omega$

$arg(Z)=arctan(\frac{X}{R})=arctan(\frac{Lw-\frac{1}{Cw}}{R})=arctan(\frac{40}{30})=53\degree$

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