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An RLC circuit such as that of Figure (a) has R = 4.17 Ohm, C - 29.4 uF, L = 0.865 H, and e_m = 26.3V.

(A) At what angular frequency w_d will the current amplitude have its maximum value, as in the resonance curves of figure (b)?

(B) what is this maximum value?

At what (C) lower angular frequency w_d1 and (D) higher angular frequency w_d2 will the current amplitude be half this maximum value?

(E) What is (w_d2 - w_d1)/w_d, the fractional half-width of the resonance curve for this circuit?

Added Thu, 25 Jun '15

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Xc=1/WC

Xl=WL

impedence of ciruit =R+(Xc-Xl)j

Current in max when impedence is min

=> Xc=Xl

=> Wd=1/sqrt(LC)=**198.07**

b)

Current, Max : 26.3/R=**6.29A**

c)For half its magnitude :

impedence=twice at peak

=> impedence= sqrt(R^2+(Xc-Xl)^2)

=>

R^2+(wL-1/wC)^2=2*4.18^2

17.47+(w*0.867-34013/w)^2=34.944

(w*0.867-34013/w)^2=17.47

=>

w*0.867-34013/w=4.18

this gives w=200.5 , 195.671

c) lower freq=**195.671**

d) higher=**200.5**

e) (200.5-195.671)/198.07

=**0.024**

Added Thu, 25 Jun '15

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