Problems solving in electrical engineering (Theoretical Foundations of Electrical Engineering), circuit analysis (Foundations of Circuit Analysis) and electronics
Main page|| Examples|| Order the problems solution|| Prices|| Guarantees||Cooperation||Contact information
Theoretical foundations of electrical engineering

Calculation of circuits with sinusoidal current (“Electric circuits of the single-phase sinusoidal current”), construction of vector and topographical diagrams

It is necessary to define in the electric circuit of the single-phase sinusoidal current which elements and parameters are specified for each case in the table:
1) resistance of the circuit and its nature;
2) RMS currents in branches;
3) voltmeter and wattmeter indications;
4) construct vector diagram of currents and topographical diagram of voltages for entire circuit.

E = 130 V;
f = 50 Hz;
R1 = 9 ohms;
L1 = 15,9 mH;
C2 = 318 μF;
L2 = 9,4 mH;
R3 = 8 ohms;
C3 = 500 μF;


Electric circuits of the single-phase sinusoidal current
Figure 1. Original scheme of the circuit. Chose arbitrary directions of currents in branches. Replace meters with its internal resistance:
Calculation of circuits with sinusoidal current
Figure 2. Design circuit

Cyclic frequency of the circuit:


Resistance of reactive components:

XL1=ωL1=314•15,9•10^(-3)=4,99 ohms;

XC2=1/(ωC2)=1/(314•318•10^(-6))=10,01 ohms;

XL2=ωL2=314•9,4•10^(-3)=2,95 ohms;

XC3=1/(ωC1 )=1/(314•500•10^(-6))=6,37 ohms;

Total resistance of the circuit:

The input resistance has active-inductive nature; it is indicated by the presence of a real part and positive imaginary part of the resistance.

Complex of the effective value of the input voltage:

E=E•(cosφ+jsinφ)=130•(cos0o+jsin0o)=130+0j V;

Rms complex currents in the circuit:

I1=E/Zвх =130/(10,632+0,669j)=12,179-0,767j=12,203•e(-4oj) A;


=7,631+2,346j=7,983•e(17oj) A;

I3=I1-I2=12,179-0,767j-7,631-2,346j=4,548-3,113j=5,511•e(-35oj) A;

Voltage drops on elements:

UL1=I1•jXL1=(12,179-0,767j)•4,99j=3,83+60,77j V;

UR1=I1•R1=(12,179-0,767j)•9=109,61-6,90j V;

UL2=I2•jXL2=(7,631+2,346j)•2,95j=-6,92+22,51j V;

UC2=I2•(-jXC2)=(7,631+2,346j)•(-10,01j)=23,48-76,39j V;

UR3=I3•R3=(4,548-3,113j)•8=36,38-24,90j V;

UC3=I4•(-jXC3)=(4,548-3,113j)•(-6,37j)=-19,83-28,97j=35,11•e(-124oj) V;

Voltmeter indications (which measures Rms voltage):

UV=UC3=35,11 V;

Wattmeter indications (which measures active power):

Pw=Re(E•I1*)=Re(130•(12,179+0,767j))=1583,3 W;

I* — conjugate current. For example, if I=a+jb, then I*=a-jb;

Constructing of Topographical diagram of voltages
Figure 3. Topographical diagram of voltages
Constructing of Vector diagram of currents
Figure 4. Vector diagram of currents
Problems solving in electrical engineering online
Copyright © 2012-2018 All rights reserved.