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

Options

A. R = 20 `Omega`, L = 1.5 H, C = 35 `mu`F
B. R = 25 `Omega`, L = 2.5 H, C = 45 `mu`F
C. R = 15 `Omega`, L = 3.5 H, C = 30 `mu`F
D. R = 25 `Omega`, L = 1.5 H, C = 45 `mu`F

Answer

c

Explanation

For better tuning the LCR circuit should have a high Q - factor of resonance , given by
Q = `(1)/(R) sqrt((L)/(C)) `
So , it should have low value of R, high value of L and low value of C. For combination (a)
` Q_(1) = (1)/(20) sqrt((1.5)/(30 xx 10^(-6))) = 11.18`
for combination (b)
`Q_(2) = (1)/(25) sqrt((25)/(45 xx 10^(-6))) = 9.43`
for combination (C)
`Q_(3) = (1)/(15) sqrt((3.5)/(30 xx 10^(-6))) = 22.77`
For combination (d)
`Q_(4) = (1)/(25) sqrt((1.5)/(45 xx 10^(-6))) = 7.3`
The highest Q-factor corresponds to combination (C).