A series AC circuit contains a resistor, an inductor of 250 mH, a capacitor of 4

Question

A series AC circuit contains a resistor, an inductor of 250 mH, a capacitor of 4.00 Mu F, and a source with Delta V max = 240 V operating at 50.0 Hz. The maximum current in the circuit is 200 mA. (a) Calculate the inductive reactance. 78.5 (b) Calculate the capacitive reactance. 723.4 What is the equation that gives the capacitive reactance? (c)Calculate the impedance. 1.25 Impedance is the effective resistance as a function of frequency. If you know the maximum current and the maximum voltage, how do you find the impedance? k (d) Calculate the resistance in the circuit. k (e) Calculate the phase angle between the current and the source voltage. o

Explanation / Answer

First we need the angular frequency omega.
Omega = 2*pi*f = 2*50*pi = 314 rad/s

(a)
Inductive reluctance (XL)= omega *L =314 * 250 x 10-3 = 78.5 ohms

(b)
Capacitive inductance (XC) = 1/(omega*C) = 1/(314 * 4 x 10^-6) = 796.18 ohms

(c)
Impedance (Z) = sqrt (R^2 + (omega*L - 1/omega*C)^2) = sqrt(1200^2 +(78.5 - 796.18)^2) = 1.4 kohms

(d)
Resistance, R = Vmax/Imax = 240/200*10-3
R = 1200 Ohms
R = 1.2 kohms

(e)
Phase angle Phi = arctan ((XL - XC)/R ) = arctan ((78.5 - 796.18)/1200) = -30.88 deg

Phi = pi - 30.88
Phi = 149.12 degree

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