An ac generator with m = 220 V and operating at 400 Hz causes oscillations in a

Question

An ac generator with m = 220 V and operating at 400 Hz causes oscillations in a series RLC circuit having R = 220 Ohm. L = 150 mH, and C = 24.0 mu F. Find (a) the capacitive reactance X_c, (b) the impedance Z, and (c) the current amplitude I. A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d) X_c, (e) Z, and (f) l increase, decrease, or remain the same. Find (a) the capacitive reactance X_c, (b) the impedance Z, and A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of New X_c, New Z Does l increase, decrease, or remain the same

Explanation / Answer

R = 220
L = 150mH
C = 24 uF
omega , w = 2*pi*f = 2*pi*400 = 800 pi
a) Xc = 1/(w*C) = (1/800*pi*24uF) = 16.5786 ohms
b) Xl = wL = 800 pi *150 mH = 376.99 ohms
Z = R + j(Xl -Xc) = 422.2525 (angle=58.6)
c) current I = V/Z = 220/422.2525   = 0.521 amps

when second capacitor is connected in series :
new C = 24/2 = 12 uF
new Xc = Xc = 1/(w*C) = (1/800*pi*12uF) = 33.1573 ohms
Z = R + j(Xl -Xc) = 408.19 ohms
As we can observe Z has decreased
I = V/Z = 220/408.19 = 0.53896 amps
ie, current increases

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