Question

At $600Hz$ , an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $60Hz$ will be

• A. $100:1$
• B. $200:1$
• C. $300:1$
• D. $400:1$

Answer 1

Answer: (A)

At $600Hz,X_C=X_L$
$\therefore \frac{1}{\omega C}=\omega L$ or ${\omega }^2=\frac{1}{LC}...(i)$
At $60Hz,\frac{X_C}{X_L}=\frac{1}{{\omega }^{\prime }C({\omega }^{\prime }L)}$
$=\frac{1}{{\omega }^{\prime 2}LC}=\frac{{\omega }^2}{{\omega }^{\prime 2}}=\frac{V^2}{V^{\prime 2}}$
(Using Eqs. $(i)$)
$=\frac{(600{)}^2}{(60{)}^2}=\frac{100}{1}$
$\therefore X_C:X_L=100:1$