R-C AND R-L IN SERIES CIRCUIT

CHAPTER 18 : ALTERNATING CURRENT CIRCUIT

Definition RC in series circuit RL in series circuit RCL in series circuit
Circuit A circuit with combination of resistor and A circuit with combination of resistor and A circuit with combination of resistor,
capacitor effect in series. inductor effect in series. capacitor and inductor effect in series.

Source The alternating current across the resistor The alternating current across the resistor The alternating current across the resistor,
current, Irms
and capacitor is the same because they are and inductor is the same because they are inductor and capacitor is the same because
Voltage across
connected in series. connected in series. they are connected in series.
(resistor and
capacitor)-RC IC = IR = Irms = I0 sin t IL = IR = Irms = I0 sin t IC = IR = IL = Irms = I0 sin t

(resistor and  Irms = I0 sin t  Irms = I0 sin t  Irms = I0 sin t
inductor)-RL
Voltage across the resistor, VR Voltage across the resistor, VR Voltage across the resistor, VR
(resistor,
capacitor and VR = V0 sin t(I and VR are in phase) VR = V0 sin t(I and VR are in phase) VR = V0 sin t(I and VR are in phase)
inductor)-RCL
Voltage across capacitor, VC Voltage across inductor, VL Voltage across capacitor, VC

VC = V0 sin(t − ) VL = V0 sin(t + ) VC = V0 sin(t −)
2 2 2

  
(VC lags I by 2 rad.) (VL leads I by 2 rad.) (VC lags I by 2 rad.)

Voltage across inductor, VL

VL = V0 sin(t +  )
2


(VL leads I by 2 rad.)

1

Prepared by
PN NOURUL SARAH BINTI ZAINUDDIN

CHAPTER 18 : ALTERNATING CURRENT CIRCUIT

Phase angle, RC in series circuit RL in series circuit RCL in series circuit
From the phasor diagram, From the phasor diagram, From the phasor diagram,

tan = VC tan = VL tan  = VL −VC
Phasor VR VR VR
diagram
tan = IXC tan = IX L tan = IX L − IXC
IR IR IR

tan = XC tan = X L tan  = X L − XC
R R R

 = tan−1 X C  = tan−1 X L  = tan−1 X L − XC
R R R

Irms leads Vrms by  rad. Vrms leads Irms by  rad. Vrms leads Irms by  rad.

Source Voltage across resistor, VR = IR . Voltage across resistor, VR = IR . Voltage across resistor, VR = IR .
voltage, Voltage across capacitor, VC = IXC . Voltage across capacitor, VL = IX L . Voltage across capacitor, VC = IXC .
From the phasor diagram above, Vrms is the From the phasor diagram above, Vrms is the Voltage across inductor, VL = IX L .
Vrms = IrmsZ resultant between VR and VC . resultant between VR and VL . From the phasor diagram above, VL and VC is
Vrms = VR2 + VC 2 VL −VC which is directed upwards since the
Vrms = VR2 + VL2 magnitude of VL is larger than VC . If VC is
Vrms = ( IR)2 + ( IXC )2 larger than VL , then VL −VC will give
Vrms = ( IR)2 + ( IX L )2 negative value which is directed downwards.
Vrms = Irms R2 + X C 2 Vrms is the resultant between VR and VL −VC .
Vrms = Irms R2 + X 2
L ( )Vrms = VR2 + VL −VC 2

Vrms = ( IR)2 + ( IX L − IXC )2

( )Vrms = Irms R2 + X L − X C 2

2

Prepared by
PN NOURUL SARAH BINTI ZAINUDDIN

CHAPTER 18 : ALTERNATING CURRENT CIRCUIT

RC in series circuit RL in series circuit RCL in series circuit

Impedance, Z By substituting Vrms = Irms R2 + XC2 By substituting Vrms = Irms R2 + X 2 By substituting Vrms = Irms R2 + ( XL − XC )2
Z = Vrms Z = Vrms L Into
Z = Vrms = V0 I rms I rms Z = Vrms
Irms I0
I rms
Into Z = Irms R2 + XC2 = R2 2 Into Z = Irms R2 + X 2 R2 2
I rms + X C L = + X L

R2 + XL − XC 2 =
I rms
I rms ( ) ( )Z = Irms
R2 + XL − XC 2
Z = R2 + XC2 Z = R2 + X 2
L

Z = R2 + ( X L − XC )2

3

Prepared by
PN NOURUL SARAH BINTI ZAINUDDIN