Question

At a frequency ${\omega }_0$ the reactance of a certain capacitor equals that of a certain inductor. If frequency is changed to 2 ${\omega }_0$ . The ratio of reactance of the inductor to that of the capacitor is

• A. 4 : 1
• B. $\sqrt{2}:1$
• C. $1:2\sqrt{2}$
• D. 1 : 2

Answer 1

The correct option is A 4 : 1

at $w_o,\frac{w_{o}L}{\frac{1}{w_{o}C}}=1$

i.e. $w_o^{2}LC=1$

now at $2w_o,\frac{2w_{o}L}{\frac{1}{2w_{o}C}}=\frac{X_L^1}{X_C^1}$

$4w_o^{2}LC=\frac{X_L^1}{X_C^1}$

$\frac{4}{1}=\frac{X_L^1}{X_C^1}$