5%20Phasor%20diagram - Passive Circuit Elements Phasor Diagram - Series RL - Series RC - Series RLC - Parallel RL - Parallel RC - Parallel RLC

Oct 25, 2026

Phasor diagrams for AC electric circuit analysis are developed for passive elements and common R, L, C configurations. The content defines voltage and current phasors in polar and rectangular forms, relates impedance additions for series RL, RC, and RLC networks, and derives resulting voltage phasors across individual components. Parallel RL, RC, and RLC cases are handled through admittance summation with currents phasors, followed by impedance and voltage/current reconstruction. Worked numeric examples compute ZT, VR, VL, VC, and corresponding phasor angles for each topology.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages18

Reading Time45 min

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Phasor diagram for the Passive Circuit Elements

Phasor diagram for series RL circuit

Phasor diagram for series RC circuit

Phasor diagram for series RLC circuit

Phasor diagram for parallel RL circuit

Phasor diagram for parallel RC circuit

Phasor diagram for parallel RLC circuit

Series-parallel AC circuit

Electric Circuits II Phasor Diagram Dr. Firas Obeidat 1 Phasor diagram for the Passive Circuit Elements Let 􀢏 (􀢚) = 􀡵 􀢓􀢉􀢕􀢙(􀣓􀢚 + 􀣘) In polar form | But Vm ∟θ and Im ∟ 􀣘 merely represent the general voltage and current phasors V and I. Thus | | | | --- | --- | --- | | | | | | The angles θ and 􀣘 are equal, so that the current and voltage are always in phase. | | | Let 􀢏 (􀢚) = 􀡵􀢓 􀢉􀢕 􀢙 􀣓􀢚 + 􀣘 = 􀡵􀢓 􀢋􀢐(􀣓􀢚+􀣘) Dr. Firas Obeidat – Philadelphia University 2 Phasor diagram for series RL circuit Example: for the circuit shown in figure (a), draw the phasor circuit , impedance diagram and voltages phasor diagram. V=100∟0, so the phasor circuit is shown in figure (b) . ZT =ZR +ZL=3Ω+j4Ω =5∟53. 13o Impedance diagram is shown in figure (c) . 􀜫 = 􀯏􀯓~~ ~~􀯍 = 505∟03~~ ~~1􀯢3o= 20∟−53. 13o VR =IZR=(20∟-53. 13oA)(3∟0Ω)=60∟-53. 13o V. VL=IZL=(20∟-53. 13o A)(4∟90Ω)=80∟36.87o V. Phasor diagram is shown in figure (d) . In rectangular form VR=60∟-53. 13o =36-j48V. VL=80∟36.87o =64+j48V. V=VR +VL=36-j48+64+j48=100+j0V=100∟0 V. 4 Dr. Firas Obeidat – Philadelphia University Phasor diagram for series RC circuit Example: for the circuit shown in figure (a), draw the phasor circuit , impedance diagram and voltages phasor diagram. I=5∟0, so the phasor circuit is shown in figure (b) . ZT =ZR +ZC=6Ω-j8Ω=10∟-53. 13o Impedance diagram is shown in figure (c) . 􀜸 = 􀜫􀜼 􀯍= (5∟53. 13o)(10∟−53. 13o )=50∟0 V VR =IZR=(5∟53.13o)(6∟0o )=30∟53.13o0 V VC =IZC=(5∟53. 13oA)(8∟-90Ω)=40∟-36.87o V. Phasor diagram is shown in figure (d) . In rectangular form VR=30∟53. 13o=18+j24 V VC=40∟-36.87o =32-j24V. V=VR +VC=18+j24+32-j24=50+j0=50∟0 V. 5 Dr. Firas Obeidat – Philadelphia University Phasor diagram for series RLC circuit Example: for the circuit shown in figure (a), draw thephasor circuit , impedance diagram and voltages phasor diagram. V=50∟0, so the phasor circuit is shown in figure (b) . ZT =ZR +ZL+ZC=3Ω+7Ω-j3Ω =3+j4= 5∟53. 13o Impedance diagram is shown in figure (c) . 􀜫 = 􀯏􀯓~~ ~~􀯍 = 5∟301􀯢3o= 10∟−53. 13o VR =IZR=(10∟−53.13o)(3∟0o )=30∟−53.13o0 V VL=IZL=(10∟-53. 13o A)(7∟90Ω)=70∟36.87o V. VC =IZC=(10∟-53. 13oA)(3∟-90Ω)=30∟-143. 13o V. Phasor diagram is shown in figure (d) . In rectangular form VR=30∟−53.13o0 V=18-j24 V VL=70∟36.87o V=56+j42 V. VC=30∟-143. 13o V=-24-j18. V=VR +VL+VC=18-j24+56+j42-24-j18 V=50+j0=50∟0 V. Dr. Firas Obeidat – Philadelphia University 6 Phasor diagram for parallel RL circuit Example: for the circuit shown in figure (a), draw thephasor circuit , impedance diagram and currents phasor diagram. V=20 ∟53 .13 , so the phasor circuit is shown in figure (b) . YT =YR +YL=1/3. 33+1/j2. 5=0. 3-j0.4 =0. 5∟-53. 13 􀜼􀜶 = 1􀯒􀯍 = 0.5~~ ~~∟53.13 =2 ∟53. 13 Impedance diagram is shown in figure (c) . 􀜫 = 􀯏􀯓~~ ~~􀯍 = 220~~ ~~.1313􀯢o= 10∟0o 􀜫 􀜴 = 􀯏􀯓~~ ~~􀯋 = 20∟53~~ ~~33.~~ ~~130~~o~~􀯢~~ ~~ = 6∟53. 13o 􀜫 􀜮 = 􀯏􀯓~~ ~~􀯅 = 20∟2~~ ~~539.~~ ~~130~~o~~􀯢~~ ~~ = 8∟−36.87o Currents Phasor diagram is shown in figure (d) . I=IR+IL=3. 6+j4. 8+6. 4-j4. 8=10+j0=10 ∟0. Dr. Firas Obeidat – Philadelphia University 7 Phasor diagram for parallel RC circuit Example: for the circuit shown in figure (a), draw thephasor circuit , impedance diagram and currents phasor diagram. I=10∟0, so the phasor circuit is shown in figure (b) . YT =YR +YC=1/1. 67+1/-j2. 5=0. 6+j0.8 =1∟53. 13 􀜼􀜶 = 1􀯒􀯍 = ~~ 1~~∟153.13 =1∟-53. 13 Impedance diagram is shown in figure (c) . 􀜸 = 􀜫􀜼 􀯍 = (10 ∟0􀝋 )(1 ∟-53. 13)= 10∟−53. 13o 􀯏 10 ∟−53. 13􀯢 􀜫 􀜴 = 􀯓􀯋 = 1. 67∟0o = 6∟−53. 13o 􀜫 􀜥 = 􀯏􀯓~~ ~~􀮼 = 10∟~~1 25~~.193􀯢0o= 8∟36.87o Currents Phasor diagram is shown in figure (d) . Dr. Firas Obeidat – Philadelphia University 8 Phasor diagram for parallel RLC circuit Example: for the circuit shown in figure (a), draw the phasor circuit , impedance diagram and currents phasor diagram. V=100 ∟53 .13 , so the phasor circuit is shown in figure (b) . YT =YR +YL+YC=1/3. 33+1/j1.

FAQs

How are voltage and current phasors represented for passive circuit elements?

Voltage and current are expressed as phasors in polar form, and the document notes that the given phasor angles correspond to the in-phase relationship between current and voltage for the passive reference used.

What is the method for series RL, RC, and RLC circuits in phasor form?

Impedances are added in series to form ZT, then component voltage phasors are calculated using VR=IZR, VL=IZL, and VC=IZC, with results provided in both polar and rectangular forms.

How are parallel RL, RC, and RLC circuits analyzed using phasors?

Admittances are summed to obtain YT, then the total current phasor and branch current phasors are computed. The impedance and resulting branch voltages or currents are then determined from the phasor relationships.

Oct 25, 2026

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