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 504030 2 2 2 2 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 2 50 100 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 53 30 40 11 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 1008060 22
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 4 30 120 A X V I C S C 3 40 120 AIII CRT 534 22 22
Phase Angle in a Parallel RC Circuit V S = 120 R = 30 X C = 40 I T = 5 A 4 A 3 A5 A 37 4 3 11 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 24 5 120 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