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 19 CHAPTER Capacitive Circuits

Topics Covered in Chapter 19  X C and R in Series  Sine-Wave V C Lags I C by 90   RC Phase-Shifter Circuit  X C and R in Parallel

Topics Covered in Chapter 19 (continued)  Sine-Wave I C Leads V C by 90   RF and AF Coupling Capacitors  Capacitive Voltage Dividers  The General Case of Capacitive Current I C

RC Voltage and Current Series Circuit The sine-wave ac voltage across a capacitor lags the capacitor’s charge and discharge currents by 90°. The sine-wave ac voltage across a resistor is always in phase with its current. The total sine-wave ac voltage for a series RC circuit always lags the total current by an angle between 0° and 90°.

 VRVR I Waveforms and Phasors for a Series RC Circuit I  I VCVC Note: since current is constant in a series circuit, the current waveforms and current phasors are shown in the reference positions.

Source Voltage and Current Phasors I Note: the source voltage lags the current by an amount proportional to the ratio of capacitive reactance to resistance. VSVS  I VSVS X C < R  I VSVS X C = R  I VSVS X C > R

Phasors for Series RC Circuits VRVR VCVC VTVT Voltage Phasors  R XCXC ZTZT Impedance Phasor 

I = 2 A The Impedance of a Series RC Circuit V S = 100 R = 30  X C = 40    C X R Z R XCXC The impedance is the total opposition to current flow. It’s the phasor sum of resistance and reactance in a series circuit A Z V I S   Z

The Tangent Function  opposite adjacent negative angle  opposite adjacent positive angle

I = 2 A The Phase Angle of a Series RC Circuit V S = 100 R = 30  X C = 40  30  40  50     Tan R X C  V S lags I by 53° I VCVC VSVS -53°

KVL in a Series RC Circuit I = 2 A V S = 100 R = 30  X C = 40  60 V 80 V 100 V V R = IR = 2 x 30 = 60 V V C = IX C = 2 x 40 = 80 V VV S 

RC Voltage and Current Parallel Circuit The sine-wave ac charge and discharge currents for a capacitor lead the capacitor voltage by 90°. The sine-wave ac voltage across a resistor is always in phase with its current. The total sine-wave ac current for a parallel RC circuit always leads the applied voltage by an angle between 0° and 90°.

Current Phasors for Parallel RC Circuits IRIR ICIC ITIT Current Phasors 

Currents in a Parallel RC Circuit V S = 120 R = 30  X C = 40  IRIR ICIC I T = 5 A ITIT A R V I S R  A X V I C S C  AIII CRT 

Phase Angle in a Parallel RC Circuit V S = 120 R = 30  X C = 40  I T = 5 A 4 A 3 A5 A    Tan I I R C  The total current leads the source voltage by 37°.

Impedance in a Parallel RC Circuit V S = 120 R = 30  X C = 40  I T = 5 A 4 A 3 A5 A  T S EQ I V Z

Summary of R, X C and Z Resistance (R) in Ohms,   Voltage in phase with current. Capacitive Reactance (X C ) in Ohms,   Voltage lags current by 90°.

Summary of R, X C and Z (continued) Series circuit impedance (Z T ) in Ohms,   Voltage lags current.  Becomes more resistive with increasing f.  Becomes more capacitive with decreasing f.

Summary of R, X C and Z (continued) Parallel circuit impedance (Z EQ ) in Ohms,   Voltage lags current.  Becomes more capacitive with increasing f.  Becomes more resistive with decreasing f.

Summary of Formulas Series RCParallel RC 22 CRT III  T S EQ I V Z  R C I I Tan  fC X C  2 1  22 CRT VVV  2 2 CT XRZ  R X Tan C  fC X C  2 1 