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RLC Circuits and Resonance - Engineering

Q1:

A certain series RLC circuit with a 200 Hz, 15 V ac source has the following values: R = 12 , C = 80 F, and L = 10 mH. The total impedance, expressed in polar form, is

A 12.2812.34° 

B 12.5712.34° 

C 9.9512.34° 

D 12.6212.34° 

ANS:A - 12.2812.34° 

Z=√R^2+(XL-XC)^2
Z=√12^2+((2*PIE*F*L)-(1/2*PIE*F*C))^2
Z=√144+12.566-9.947.

Z=12.28 ohm.

FOR ANGLE θ due to Polar Form as Required,
θ = tangent inverse*(XL-XC/R).
= tan.inv*(12.566-9.947/12).
= 12.31.
So,
= 12.28<12.31* ohm , Option A.