At which frequency has the impedance its smallest value (resonance frequency)? C

Question

At which frequency has the impedance its smallest value (resonance frequency)?

Calculate the impedance at the resonance frequency.

Tries 0/6 An RLC circuit with a resistance of 79 ?, a capacitance of 6.6 microF and an inductance of 60 mH is connected to an ac voltage supply which has an angular frequency of ?d= 64 rad/s. Calculate the inductive reactance of the circuit. At which frequency has the impedance its smallest value (resonance frequency)? Calculate the impedance at the resonance frequency.

Explanation / Answer

a. inductivr reactance XL = 2pifL = wL = 64*60*10^-3 = 3.84 ohms

b. w^2 = 1/LC = 1/(0.06 * 6.6*10^-6)

w =2pif = 794 rad/s

f= 794/82*3.14) = 126.5 Hz

c. impedence Z^2= R^2 +(XL-XC)^2

at resonance XL= Xc

so Z= R = 79 ohms

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