Creating Phasor Diagrams with Circuit Magic

Phasor diagram

Step 1. Construct following circuit using Circuit Magic schematics editor.

R1=10 ohms; R2=10 ohms; R3=10 ohms;

L1=0,2H; �1=200mkF; E1=100 V;

Step 2. Run Node Voltage simulation.

Solution

V1�Y11=I11

Branches impedance calculation

Z1=R2+j�w�L1=10+j�314,2�0,2=10+j62,83

Z2=R1+j�-1/(w�C1)=10+j�-1/(314,2�200�10^-6)=10-j15,92

Z3=R3=10=10

Y11=1/Z1+1/Z2+1/Z3=0,1308+j0,02953

I11=-E1/Z3=(-100)/(10)=-10

(0,1308+j0,02953)�j₁=-10

j₁=-72,76+j16,43

j₂=0

I1=(V1-V2)/Z1=0,07524+j1,17

I2=(V1-V2)/Z2=-2,799-j2,813

I3=(V1-V2+E1)/Z3=2,724+j1,643

Step 3. Select Create Phasor diagram Menu item.

Step 5 Change phasors graphics properties.

By using phasor diagram above we can easily check solution.

1. Kirchhoff�s Currents Law.

Vector sum of f the currents in all the branches which converge in a common node is equal to zero

(Vector sum of currents phasors I1,I2,I3 is equal to zero)

2. Kirchhoff�s Voltage Law.

Make use of following rules to find mistakes in analysis.

Rule 1.

Phasors of resistance voltage and current through resistance are parallel to each other.

(∆UR1 &I2 , ∆UR3 &I3 , ∆UR2 &I1 ,)

Rule 2.

Rule 3.

Phasors of capacitance voltage and current through resistance are perpendicular to each other. (Current leads voltaget).