Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz

Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 18 CHAPTER Capacitive Reactance

Topics Covered in Chapter 18  Alternating Current in a Capacitive Circuit  The Amount of X C Equals 1/(2  fC)  Series and Parallel Capacitive Reactance  Ohm's Law Applied to X C  Applications of Capacitive Reactance  Sine-Wave Charge and Discharge Current

Definitions Capacitive reactance is the opposition a capacitor offers to the flow of sinusoidal current.  Symbol: X C  Units: Ohms  Formula: X fC C  1 2 

The value of X C is inversely proportional to the value of capacitance:  Increasing C decreases X C  Decreasing C increases X C The value of X C is inversely proportional to the frequency:  Increasing f decreases X C  Decreasing f increases X C Factors Affecting X C

Factors Affecting Alternating Current Flow Less reactance means more current flow.

Summary of X C Formulas When f and C are known: X fC C  1 2  C fX C  1 2  f CX C  1 2  When X C and f are known: When X C and C are known:

Capacitive Reactances in Series Total reactance is the sum of the individual reactances. X CT = X C1 + X C2 + X C etc. All reactances have the same current. The voltage across each reactance equals current times reactance. V XC1 = I  X C1

2  F 5  F 10  F C T = 1.25  F C1C1 C3C3 C2C2 1 kHz X C 1 = 1/(2  fC 1 ) = 1/(6.28 x 1x10 3 x 10x10 -6 ) = 15.9  X C 2 = 1/(2  fC 2 ) = 1/(6.28 x 1x10 3 x 5x10 -6 ) = 31.8  X C 3 = 1/(2  fC 3 ) = 1/(6.28 x 1x10 3 x 2x10 -6 ) = 79.6  X C T = = 127  Capacitive Reactances in Series X C T = 1/(2  fC T ) = 1/(6.28 x 1x10 3 x 1.25x10 -6 ) = 127 

2  F 5  F 10  F C T = 1.25  F C1C1 C3C3 C2C2 1 kHz 127 V V C 1 = IX C 1 = 1 x 15.9 = 15.9 V Ohm’s Law I = V/X C T = 127/127 = 1 A V C 2 = IX C 2 = 1 x 31.8 = 31.8 V V C 3 = IX C 3 = 1 x 79.6 = 79.6 V KVL check: = 127 V

Capacitive Reactances in Parallel Total reactance is found by the reciprocal formula: XXXX etc CTCCC  . All reactances have the same voltage. The current through each reactance equals voltage divided by reactance. I C = V C / X C

Capacitive Reactances in Pparallel 2  F5  F10  F C EQ = 17  F 1 kHz 127 V C1C1 C3C3 C2C2 I C 1 = 127/X C 1 = 127/15.9 = 7.99 A I C 2 = 127/X C 2 = 127/31.8 = 3.99 A I C 3 = 127/X C 3 = 127/79.6 = 1.60 A I T = 127/X C EQ = 127/9.36 = 13.6 A KCL check: = 13.6 A

Capacitance vs. Capacitive Reactance Capacitance Symbol is C Unit is F Value depends on construction i C = C(dv/dt) Capacitive Reactance Symbol is X C Unit is  Value depends on C and f X C = v c / i c or 1/(2  fC)

Capacitor Current as a Function of dv/dt i C = 1x10 -6 (6000) = 6 mA Triangle generator 1  F 0 V 6 V 1 ms + 6 mA - 6 mA i C = C(dv/dt) i C = 1x10 -6 (-6000) = -6 mA time iCiC vCvC

dv/dt for Sinusoidal Voltage is a Cosine Wave Voltage 0  dv/dt V inst. = V max x cos  Sine wave

Capacitive Reactance vs. Resistance Capacitive Reactance Symbol is X C Unit is  Value decreases for higher f Current leads voltage by 90° (  = 90°) Resistance Symbol is R Unit is  Value does not change with f Current and voltage are in phase (  = 0°)

Capacitor Voltage and Current Amplitude 0  I V I V Time

Resistor Voltage and Current Amplitude 0  I V V Time I