Apr 21,2023
Please explain series resonance, parallel resonance, series-parallel resonance and calculation formula
Resonance is a phenomenon that occurs in AC circuits when the frequency of the applied voltage is equal to the natural frequency of the circuit. When resonance occurs, the circuit can absorb more energy than it would at other frequencies, and the current and voltage amplitudes can become very large.
There are three types of resonance in circuits: series resonance, parallel resonance, and series-parallel resonance.
Series resonance occurs in a circuit where the inductor and capacitor are connected in series. The impedance of the circuit is at a minimum when the frequency of the applied voltage is equal to the resonant frequency of the circuit. The formula for calculating the resonant frequency is:
f = 1 / (2π √(LC))
Where f is the resonant frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads.
Parallel resonance occurs in a circuit where the inductor and capacitor are connected in parallel. The impedance of the circuit is at a maximum when the frequency of the applied voltage is equal to the resonant frequency of the circuit. The formula for calculating the resonant frequency is:
f = 1 / (2π √(LC))
where f is the resonant frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads.
Series-parallel resonance occurs in a circuit where some components are connected in series and others are connected in parallel. The resonant frequency of the circuit can be calculated by finding the resonant frequency of the series components and the parallel components and then finding the harmonic mean of the two frequencies. The formula for calculating the resonant frequency is:
f = 1 / (2π √(L_eq C_eq))
where f is the resonant frequency in Hertz, L_eq is the equivalent inductance of the series components, and C_eq is the equivalent capacitance of the parallel components. The equivalent inductance and capacitance can be calculated using the following formulas:
L_eq = L1 + L2 + ... + Ln
C_eq = (C1^-1 + C2^-1 + ... + Cn^-1)^-1
where L1, L2, ..., Ln are the inductances of the series components and C1, C2, ..., Cn are the capacitances of the parallel components.
