Capacitive Reactance Rubber Sheet Flow in a pipe

Capacitive Reactance

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

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. v C

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 v

Frequency Dependent XC ] Resistance in a resistor is the same for all frequencies. ] Capacitive reactance depends inversely on frequency. f • High reactance at low frequency • Low reactance at high frequency

Audio Cutoff ] Find the capacitive reactance of a 0. 100 m. F 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/(2 p 102 Hz 10 -7 F)= 16 k. W • 1/(2 p 108 Hz 10 -7 F)= 16 m. W ] 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 next