Which of the following combinations should be selected for better turning of an LCR circuit used for communication ?

Options

A. `R = 20 Omega ,L = 1.5H, C = mu F`
B. `R = 25 Omega , L = 2.5 H,C = 45muF`
C. `R = 15Omega, L = 3.5 H, C = 30 mu F`
D. `R = 25 Omega, L = 1.5H, C = 45 mu F`

Answer

C

Explanation

Quality factor of an LCR circuit is given by
`Q = 1/R sqrt(L/C)`
` Q_1 = 1/20 sqrt((1.5)/(35 xx 10^(-6) )) = 50 xx sqrt(3/70) = 10/35`
`Q_2 = 1/25 xx sqrt((2.5)/(45 xx 10^(-6))) = 40 xx sqrt(5/90) = 9.43`
`Q_3 = 1/15 sqrt((3.5)/(30 xx 10^(-6)) ) = 100/15 sqrt(35/3) = 22.77`
`Q_4= 1/25 xx sqrt((1.5)/(45 xx 10^(-6)) ) = (40)/(sqrt30) = 7.30`
Clearly `Q_3` is maximum of `Q_1 , Q_2 , Q_3` and `Q_4` .