Download Capacitive Reactance

Capacitive Reactance
Rubber Sheet
 Flow in a pipe can be blocked
by an elastic membrane.
rvA
• Provides restoring spring force
F (t )  kx(t )
 A capacitor blocks the flow of
direct current.
• Gap between plates
 The charge provides a
i
restoring potential.
• AC current can flow
C
V (t )  
Q(t )
C
AC Driver
 An AC source provides a
sinusoidal voltage.
• Capacitor matches
• One loop circuit
v
C
vC  V0 sin t
 The capacitor charge varies
with the voltage.
 The current is related to the
rate of change of the charge.
qC  CV0 sin t
i
q
 CV0 cos t
t
Phase Shift
 Voltage and current are not in phase through a capacitor.
• Current leads voltage: ICE man
Almost Ohm
 The amplitude of voltage and
current through a capacitor are
related.
 The ratio gives an expression
like Ohm’s law.
 This is the capacitive
1
C
v
vC  V0 sin t  V0
i  CV0 cos t  CV0
reactance.
• Measured in ohms
XC 
vC
i

V0
1

CV0 C
Frequency Dependent
XC
1
XC 
2fC
 Resistance in a resistor is the
same for all frequencies.
 Capacitive reactance depends
inversely on frequency.
• High reactance at low
frequency
• Low reactance at high
frequency
f
Audio Cutoff
 Find the capacitive reactance
of a 0.100 mF capacitor at an
audio frequency of 100 Hz and
at an FM-radio frequency of
100 MHz.
 The formula for capacitive
reactance depends on
frequency.
• Frequency f in Hz
XC 
1
1

C 2fC
 Find the reactance in ohms.
• 1/(2 102 Hz 10-7F)= 16 kW
• 1/(2 108 Hz 10-7F)= 16 mW
 Note that there is virtually no
resistance at radio frequency.
Extreme Behavior
 At low frequency the capacitive reactance is high.
• Like high resistance
• Open circuit element – capacitor plates
 At high frequency the capacitive reactance is low.
• Like low resistance
• Closed circuit element – ideal conductor
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