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a c
ohms and the short-circuit equivalent can be applied, resulting in V C �
0 V and v C � �90°, and producing the phasor diagram of Fig. 15.51.
The network is then resistive, the phase angle between I and E is essentially
zero degrees, and V R and I are their maximum values.
A plot of V C versus frequency appears in Fig. 15.52. At low frequencies
X C >> R, and V C is very close to E in magnitude. As the
10
9
8
7
6
5
4
3
2
1
V C
Network capacitive
V C ( f )
0 1 5
10
15 20 f (kHz)
FREQUENCY RESPONSE OF THE R-C CIRCUIT ⏐⏐⏐ 653
Network resistive
FIG. 15.52
The magnitude of the voltage V C versus frequency for the circuit of Fig. 15.45.
applied frequency increases, X C decreases in magnitude along with V C
as V R captures more of the applied voltage. A plot of v C versus frequency
is provided in Fig. 15.53. At low frequencies the phase angle
–30°
–60°
–90°
θC
(phase angle between E and VC )
0 1 5
10 15 20 f (kHz)
Network capacitive
θC
( f )
Network resistive
FIG. 15.53
The phase angle between E and V C versus frequency for the circuit of
Fig. 15.45.
VR vI ≅ 0°
VC ≅ 0 V E vC ≅ –90°
f = very high frequencies
FIG. 15.51
The phasor diagram for the circuit of Fig.
15.45 at very high frequencies.