A 100 V, AC source of frequency 500 Hz is connected to an LCR circuit with `L = 8.1 mH`, `C = 12.5 mu F, R = 10 Omega` all connected in series as shown in the figure. What is the quality factor of the circuit?

Options

A. `2.02 `
B. `2.54 `
C. `50.54 `
D. `200.54 `

Answer

B

Explanation

The quality factor of the series LCR circuit is `Q = (1)/(R) sqrt ( (L )/(C))`
On putting the given values,
`Q = (1)/(10) sqrt (( 8.1 xx 10 ^(-3))/ ( 12. 5 xx 10 ^(-6)))= (1)/(10) sqrt (( 81 xx 1000)/( 125))`
`= (9)/(5) sqrt2 = 2. 54`