Two inductors of 40mH and 50mH: Calculate
a) The total inductance when in series [3]
b) The total inductance when in parallel [3]
c) Determine the resonant frequency and magnification factor Q of a series RLC circuit in which R= 47Ω, L=12 mH and C= 65pF.
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90 mH in Series , 22.22 mH in Parallel , resonant frequency = 180 khz , magnification factor Q = 289
Explanation:
ignoring mutual inductance
in Series 40 + 50 = 90 mH
in Parallel = 1/(1/40 + 1/50) = 200/(5 + 4) = 200/9 = 22.22 mH
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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