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Question
A 0.1 H inductor a 25 × 10-6 F capacitor and a 15 Ω resistor are connected in series to a 120 V, 50 Hz AC source. Calculate the resonant frequency.
Solution
Given Data:
- Inductance, L = 0.1 H
- Capacitance, C = 25 × 10−6 F
- Resistance, R = 15 Ω (not required for resonance calculation)
`f_r = 1/(2pi sqrt((0.1)(25xx10^-6)))`
Calculate LC:
LC = (0.1) × (25 × 10 − 6) = 2.5 × 10−6
Take the square root:
`sqrt(LC) = sqrt(2.5xx10^-6) = 1.581xx10^-3`
Calculate the reciprocal: `f_r = 1/(2pi (1.581 xx 10^-3))`
`f_r = 1/(9.934xx10^-3)`
= 100.7 Hz
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