Question

An AC generator producing 10V(rms) at 200 rad/s is connected in series with a $50\Omega$ resistor, a 400 mH inductor and a $200\mu F$ capacitor. The rms voltage across the inductor is

• A. 2.5 V
• B. 3.4 V
• C. 6.7 V
• D. 10.8 V

Answer 1

Answer: (D)

Given $E=10V$
$\omega =200rad/s$
$R=50\Omega$
$L=400mH$
$C=200\mu F$
We know that,
$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$
$=\sqrt{(50{)}^2+(80-25{)}^2}=\sqrt{(50{)}^2-(55{)}^2}$
$=\sqrt{2500+3025}$
$Z=\sqrt{5525}=74.3\Omega$
$I=\frac{E}{Z}=\frac{10}{74.3}=0.13459A$
$E_L=I{X}_L=0.13459\times 80$
$=10.76V\text{ or }10.8V$