Question

For the circuit shown, find the impedance and phase angle. Draw an impedance phasor diagram and fill in the table below. Is the circuit inductive, capacitive, or (nearly) purely resistive?

Answer 1

Inductive reactance=$X_L=\omega L=2\pi f L=2\pi \times 240\times 25\times 10^{-3}=37.7\Omega$

Capacitive reactance =$X_C=\frac{1}{\omega C}=\frac{1}{2\pi f C}=\frac{1}{2\pi \times 240\times 15\times 10^{-6}}=44.21\Omega$

So impedance of LCR circuit is

$Z=\sqrt{R^2+(X_L-X_C)^2}=\sqrt{15^2+(37.7-44.21)^2}=16.35\Omega$

Phase is

$cos\phi=\frac{R}{Z}\\ \implies \phi=cos^{-1}\left(\frac{R}{Z} \right )\\ \implies \phi=cos^{-1}\left(\frac{15}{16.35 } \right )\\ \implies \phi=23.44\degree$

For Resistor

$I_{rms}=\frac{V}{Z}=\frac{20}{16.35}=1.22A$

$V_{rms}=I_{rms}R=1.22\times 15=18.3V$

$P=VI=18.3\times1.22=22.326W$

For inductor

$I_{rms}=\frac{V}{Z}=\frac{20}{16.35}=1.22A$

$V_{rms}=I_{rms}X_L=1.22\times 37.7=45.994V$

$P=VI=45.994\times1.22=56.11W$

For Capacitor

$I_{rms}=\frac{V}{Z}=\frac{20}{16.35}=1.22A$

$V_{rms}=I_{rms}X_C=1.22\times 44.21=53.94V$

$P=VI=53.94\times1.22=65.61W$

Phasor diagram

V R

Circuit is capactive