At a certain frequency ω1, the reactance of a certain capacitor equals to that of a certain inductor. If the frequency is changed to ω2=2 ω1, the ratio of the reactance of the inductor to that of the capacitor is .

Question

At a certain frequency ω1, the reactance of a certain capacitor equals to that of a certain inductor. If the frequency is changed to ω2=2 ω1, the ratio of the reactance of the inductor to that of the capacitor is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

At a certain frequency ω1, XL1=XC1, ω1 L=(1/ω1 C) Now, frequency is changed to XL2=ω2 L=2 ω1 L=2((1/ω1 C))=2((2/ω2 C))=4 × C2 Ratio of reactance of inductor to capacitor, i.e. (XL2/XC2)=4

Q. At a certain frequency ω1​, the reactance of a certain capacitor equals to that of a certain inductor. If the frequency is changed to ω2​=2ω1​, the ratio of the reactance of the inductor to that of the capacitor is _______.

At a certain frequency ω1​,XL1​​=XC1​​,ω1​L=ω1​C1​ Now, frequency is changed to XL2​​=ω2​L=2ω1​L=2(ω1​C1​)=2(ω2​C2​)=4×C2​ Ratio of reactance of inductor to capacitor, i.e. XC2​​XL2​​​=4

Q. At a certain frequency $ω_{1}$ , the reactance of a certain capacitor equals to that of a certain inductor. If the frequency is changed to $ω_{2} = 2 ω_{1}$ , the ratio of the reactance of the inductor to that of the capacitor is _______.