Capacitive reactance
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Capacitive Reactance. Flow in a pipe can be blocked by an elastic membrane. Provides restoring spring force A capacitor blocks the flow of direct current. Gap between plates The charge provides a restoring potential. AC current can flow. Rubber Sheet. r vA. i. C.

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Rubber sheet

Flow in a pipe can be blocked by an elastic membrane.

Provides restoring spring force

A capacitor blocks the flow of direct current.

Gap between plates

The charge provides a restoring potential.

AC current can flow

Rubber Sheet

rvA

i

C


Ac driver

An AC source provides a sinusoidal voltage.

Capacitor matches

One loop circuit

The capacitor charge varies with the voltage.

The current is related to the rate of change of the charge.

AC Driver

v

C


Phase shift
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 reactance.

Measured in ohms

Almost Ohm

v


Frequency dependent

Resistance in a resistor is the same for all frequencies. related.

Capacitive reactance depends inversely on frequency.

High reactance at low frequency

Low reactance at high frequency

Frequency Dependent

XC

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

Find the reactance in ohms.

1/(2p 102 Hz 10-7F)= 16 kW

1/(2p 108 Hz 10-7F)= 16 mW

Note that there is virtually no resistance at radio frequency.

Audio Cutoff


Extreme behavior
Extreme Behavior audio frequency of 100 Hz and at an FM-radio frequency of 100 MHz.

  • 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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