An RLC circuit such as that of Figure ( a ) has R = 4.30 ?, C = 19.1 ?F, L = 1.4

Question

An RLC circuit such as that of Figure (a) has R = 4.30 ?, C = 19.1 ?F, L = 1.43 H, and ?m = 33.7 V. (a) At what angular frequency ?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 ?d1 and (d) higher angular frequency ?d2 will the current amplitude be half this maximum value? (e) What is (?d2 - ?d1)/?d, the fractional half-width of the resonance curve for this circuit?

EAT_1292342783771_0_7939092050372686.gif

fig31_13.gif

A)____Rads/s

B)____A

C)____Rad/s

D)____Rad/s

E)____

An RLC circuit such as that of Figure (a) has R = 4.30 ?, C = 19.1 ?F, L = 1.43 H, and ?m = 33.7 V. (a) At what angular frequency ?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 ?d1 and (d) higher angular frequency ?d2 will the current amplitude be half this maximum value? (e) What is (?d2 - ?d1)/?d, the fractional half-width of the resonance curve for this circuit?

Explanation / Answer

a) resonant frequency will be, w= 1/sqrt(LC)= 1/(1.43*19.1 *10^-6)

=191.34 rad/s

b) maximum vamule of current= em/r

= 33.7/4.3

7.84A

c)

quality factor Q, = wL/R= 191.34*1.43/4.3

=63.66

therefore w/(w2-w1)= Q= 63.66

=> w2-w1= 193.34/63.66

=3.04

c) therefore lower frequency w1- 193.34-3.04/2

= 191.82 rad/s

D)

higher frequency w2= 194.86 rad/s

(E) w2-w1)/w= 1/Q= 1/63.66 = 0.016

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