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ƒ r<br />

E = 10 V ∠0°<br />

+<br />

–<br />

I<br />

+ –<br />

V R<br />

+ VL –<br />

R = 2 � X L = 10 �<br />

FIG. 20.19<br />

Example 20.1.<br />

X C = 10 �<br />

Solutions:<br />

a. ZTs � R � 2 �<br />

E 10 V �0°<br />

I ����� �5 A �0°<br />

ZTs 2 � �0°<br />

VR � E � 10 V �0°<br />

VL � (I �0°)(XL �90°) � (5 A �0°)(10 � �90°) � 50 V �90°<br />

VC�(I �0°)(XC��90°)�(5 A �0°)(10 � ��90°)�50 V ��90°<br />

XL 10 �<br />

b. Qs � � ��� 5<br />

R 2 �<br />

fs 5000 Hz<br />

c. BW � f2 � f1 � � ��� 1000 Hz<br />

Qs 5<br />

1<br />

�<br />

2<br />

d. P HPF � P max � I 2 maxR � �� (5 A) 2 (2 �) � 25 W<br />

EXAMPLE 20.2 The bandwidth of a series resonant circuit is 400 Hz.<br />

a. If the resonant frequency is 4000 Hz, what is the value of Qs? b. If R � 10 �, what is the value of XL at resonance?<br />

c. Find the inductance L and capacitance C of the circuit.<br />

Solutions:<br />

fs fs 4000 Hz<br />

a. BW � � or Qs ����� 10<br />

Qs<br />

BW 400 Hz<br />

X L<br />

1<br />

�<br />

2<br />

b. Qs � �<br />

R<br />

or XL � QsR � (10)(10 �) � 100 �<br />

c. XL � 2pfsL or<br />

XL 100 �<br />

L ����� � 3.98 mH<br />

2pfs 2p(4000 Hz)<br />

1<br />

XC � �<br />

2pfsC<br />

or<br />

1<br />

1<br />

C ������ 2pfsXC 2p(4000 Hz)(100 �)<br />

� 0.398 mF<br />

1<br />

�<br />

2<br />

EXAMPLE 20.3 A series R-L-C circuit has a series resonant frequency<br />

of 12,000 Hz.<br />

a. If R � 5 �, and if XL at resonance is 300 �, find the bandwidth.<br />

b. Find the cutoff frequencies.<br />

Solutions:<br />

XL 300 �<br />

a. Qs � � ��� 60<br />

R 5 �<br />

fs 12,000 Hz<br />

BW ����� �200 Hz<br />

Qs 60<br />

+<br />

–<br />

V C<br />

EXAMPLES (SERIES RESONANCE) ⏐⏐⏐ 899

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