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Find the impedance if the frequency is 1kHz for the parallel alarm system if R = 3.3kohms, C = 0.02 uF, L = 100mH

Please assist thank you.

2 answers

Z = R + j(Xl-Xc).

R = 3300 ohms.
Xl = 2pi*F*L = 628 ohms.
Xc = 1/(2pi*F*C) = 7958 ohms.

Z = 3300+j(628-7958)
Z = 3300-j7330 = 8038 ohms[-65o].
Parallel RLC Circuit
X = Xl*Xc/(Xl-Xc) = 628*7958/(-7958+628) = -j682 ohms. = 682[-90].
Z = R*X/(R-jX) = 3300*682[-90]/(3300-j682)
Z = 3300*682[-90]/3370[-12o] = 668 ohms[-78o].