Question

Determine the resonant frequency and magnification factor Q of a series RLC circuit in which R= 47Ω, L=12 mH and C= 65pF

Answer 1

resonant frequency   = 180 khz ,  magnification factor Q  = 289

Explanation:

Resonant frequency  = 1/2π√LC

( ∵ at Resonant frequency XL =  Xc  => 2πfL = 1/2πC   => f =  1/2π√LC)

L = 12 mH = 12 * 10⁻³  L

C = 65 pF  = 65 * 10⁻¹²  F

f = 1/2π√(12 * 10⁻³ * 65 * 10⁻¹²)

=> f =  1/2π√(78 *10⁻¹⁴)

=> f =  1/2π√(78 *10⁻¹⁴)

=> f =  1/2π 78 *10⁻¹⁴)

=> f = 1.8 * 10⁵

=> f  = 180 khz

the resonant frequency   = 180 khz

Q = (Reactive Power/Average Power)

Q  = XL/R  =  Xc/R  =  2π fr * L/R

Q = (1/R) √L/C

Q =  (1/47) √(12 * 10⁻³  / 65 * 10⁻¹² )

=> Q = 289

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Answer 2

Answer:

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