LCR circuit, the resonance frequency of circuit increases two times of the initial circuit by changing C and C' and R from `100 Omega " to " 400 Omega` while the inductance was kept the same. The ratio C/C', is

Options

A. 2
B. 8
C. 16
D. 4

Answer

D

Explanation

Given ,
in series LCR circuit ,
initial capacitance , `C_1 = C'`
Final value of capacitance , `C_2 = C'`
indutance , `L_1 = L_2 = L`
and resistance , `R_1 = 100 Omega`
` R_2 = 400 Omega`
` therefore ` Resonance frequency
` f_1 = (1)/(2pi sqrt (L__1C_1) ) rArr f_1 = (1)/(2pi sqrt(LC) )`
and ` f_2 = (1)/(2pi sqrt(L_2C_2) ) rArr f_2 = (1)/(2pi sqrt(L.C') )`
Given ` f_2 = 2f_1 rArr (1)/(2pi sqrt(LC') ) = (2)/(2 pi sqrt (LC) )`
`(1)/(sqrt(C')) = (2)/(sqrtC) rArr (1)/(C') = 4/C rArr (C )/(C') = 4`