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a c
Therefore,
E � �(1�3�.3�0� V�) 2 � �� (�1�4�.8�6� V�) 2 � � 20 V
and vE � 0° (from phasor diagram)
and E � 20 �0°
Z (10 � �0°)(20 V �0°) 200 V�0°
f. VR �� RE
���� ���
ZT 15 � �48.16° 15 �48.16°
� 13.3 V ��48.16°
Z (26.5 � ��90°)(20 V �0°) 530.6 V��90°
VC �� CE
���� ���
ZT 15 � �48.16°
15 �48.16°
� 35.37 V ��138.16°
15.5 FREQUENCY RESPONSE OF THE
R-C CIRCUIT
Thus far, the analysis of series circuits has been limited to a particular
frequency. We will now examine the effect of frequency on the response
of an R-C series configuration such as that in Fig. 15.45. The magnitude
of the source is fixed at 10 V, but the frequency range of analysis will
extend from zero to 20 kHz.
+
E = 10 V ∠ 0°
f : 0 to 20 kHz –
Z T
R
5 k�
C
+
0.01 mF VC –
FIG. 15.45
Determining the frequency response of a series R-C circuit.
ZT Let us first determine how the impedance of the circuit ZT will
vary with frequency for the specified frequency range of interest.
Before getting into specifics, however, let us first develop a sense for
what we should expect by noting the impedance-versus-frequency
curve of each element, as drawn in Fig. 15.46.
At low frequencies the reactance of the capacitor will be quite high
and considerably more than the level of the resistance R, suggesting that
the total impedance will be primarily capacitive in nature. At high frequencies
the reactance XC will drop below the R � 5-k� level, and the
network will start to shift toward one of a purely resistive nature (at
5k�). The frequency at which XC � R can be determined in the following
manner:
1
XC ���R 2pf1C
and
1
f1 � �
2pRC
�
X C � R
FREQUENCY RESPONSE OF THE R-C CIRCUIT ⏐⏐⏐ 647
(15.11)