Question

A $300\Omega$ resistor, a $0.250H$ inductor, and a $8.00\mu F$ capacitor are in series with an ac source with voltage amplitude $120V$ and angular frequency $400rad/s$. Which of the following is/are correct?

• A. Voltage amplitude across the resistor is $97.9V$
• B. Voltage amplitude across the inductor is $32.6V$
• C. Voltage amplitude across the capacitor is $102V$
• D. Voltage amplitude across the resistor is $32.6V$

Answer 1

Answer: (A), (B), (C)

The correct options are
A Voltage amplitude across the resistor is $97.9V$
B Voltage amplitude across the capacitor is $102V$
C Voltage amplitude across the inductor is $32.6V$

$X_L=\omega L=400\times 0.25=100\Omega$
$X_C=\frac{1}{\omega C}=\frac{1}{400\times 8\times {10}^{-6}}=312.5\Omega$
$Z=\sqrt{R^2+(X_C-X_L{)}^2}$
$=\sqrt{(300{)}^2+(312.5-100{)}^2}=368\Omega$

$I_o=\frac{V_o}{Z}=\frac{120}{368}=0.326A$

$(V_0{)}_R=I_{0}R=0.326\times 300=97.8V$
$(V_0{)}_L=I_0{X}_L=0.326\times 100=32.6V$
$(V_0{)}_C=I_0{X}_C=0.326\times 312.5=102V$