A series AC circuit contains a resistor an inductor of 230 m

A series AC circuit contains a resistor, an inductor of 230 mH, a capacitor of 5.90 µF, and a source with V_max = 240 V operating at 50.0 Hz. The maximum current in the circuit is 180mA.

(a) Calculate the inductive reactance.


(b) Calculate the capacitive reactance.


(c) Calculate the impedance.
k

(d) Calculate the resistance in the circuit.
k

(e) Calculate the phase angle between the current and the source voltage.

Solution

here, V_max = 240 V, I_max = 180 * 10^-3 A, L = 230 * 10^-3 H, C = 5.90 * 10^-6F, and f = 50 Hz

a) inductive reactence is,

           X_L = L = 2fL = 72.22

b) capacitve reactence:

           X_C = 1/C = 1/2fC = 539.78

c) impedence of the circuit, Z = V_max/ I_max = 1333.33 = 1.33 k

d)

Thus, the resistance is,

               R = sqrt[ Z^2 - (XL - Xc)^2.] = 1248.66 = 1.248 k

e) phase angel = tan^-1 ( X_L- X_C)/R = -20.528⁰