RLC Series Circuit

Frequency: Hz
Voltage: cos(ωt + ° )
Resistance:
Coil:
Capacitor:
 
Round:
 

 

Calculations

ω:314,16 rad/s
Reactance coil:157,08 j
Reactance capacitor:-159,15 j
Total reactance:-2,08 j
 
 
Series-resonance-angular-frequency:316,23 Hz
Series-resonance-frequency:50,33 Hz
 
 
φ:-14,54°
Z:8 + -2,08 j = 8,26 ∠ -14,54°
 
 
Current:27,83 cos(ωt + 14,54°) A
 
 
 
Complex power6.400,64 VA
Real power6.195,57 W
Reactive power1.607,22 VAr
 
 
 
Impedance triangle:

 
 
Replacement circuit:
8 Ω
0.0015337940978902 F

 

Formulas
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Angular frequency

ω = 2 π f
ω: Angular frequency (rad/s)
f: frequency (Hz)


Reactance coil

XL = j ω L
XL: Reactance coil (Ω)
ω: Angular frequency (rad/s)
L: Coil inductance (H)


Reactance capacitor

XC =1
j ω C
XC: Reactance capacitor (Ω)
ω: Angular frequency (rad/s)
C: Capacitor capacitance (F)


Series resonance angular frequency

ωres = 1
√(L C)
ωres: Resonance angular frequency (rad/s)
L: Coil inductance (H)
C: Capacitor capacitance (F)


Power factor (φ)

φ = atan(Xtotal)
R
φ: Power factor
Xtotal: Total reactance (Ω)
R: Resistance (Ω)


Total impedance

Z = √(Xtotal² + R²) ∠ φ
Z: Total impedance
Xtotal: Total reactance (Ω)
R: Resistance (Ω)
φ: Power factor


Current

I =U
Z
I: Current (A)
U: Voltage (V)
Z: Total impedance


Complex power

S =U I
S: Complex power (VA)
U: Voltage (V)
I: Current (A)


Real power

P =U I cos(φ)
P: Real power (W)
U: Voltage (V)
I: Current (A)
φ: Power factor


Reactive power

Q =U I sin(φ)
P: Reactive power (VAr)
U: Voltage (V)
I: Current (A)
φ: Power factor