# Phasor Diagram for Series RLC Circuits

Phasor Diagram for Series RLC Circuits

This Demonstration shows a phasor diagram in an AC series RLC circuit. The circuit consists of a resistor with resistance , an inductor with inductance , and a capacitor with capacitance . The current in an RLC series circuit is determined by the differential equation

R

L

C

I

E

0

R+j(-)

X

L

X

C

where and is the AC emf driving the circuit. The angular frequency is related to the frequency in hertz (Hz) by . In this Demonstration, the amplitude is set to 10 volts (V). You can vary the frequency in Hz, the resistance in ohms (), the inductance in millihenries (mH), and the capacitance in microfarads (F).

j=

-1

e(t)=sin(ωt)

E

0

ω

f

ω=2πf

E

0

f

R

Ω

L

C

μ

X

L

X

C

1

ωC

V

R

I

V

L

X

L

I

V

C

X

C

I

The phase of is the same as that of . leads . The phase of lags that of by .

V

R

I

V

L

I

by

0

90

V

C

I

0

90

The voltage and current are out of phase by an angle , where

φ

tanφ=-

X

L

X

C

R

When > the effect of inductance is dominant; then , and the RLC circuit's total voltage =++=(R+j-j) leads the current . When <, the capacitance contribution is dominant, , and the current leads the voltage. When the circuit has a pure resistance or when the resonance condition = or is satisfied, then , meaning that the voltage and current are in phase.

X

L

X

C

,

φ>0

V

V

R

V

L

V

C

X

L

X

C

I

I

X

L

X

C

φ<0

X

L

X

C

ω=

1

LC

φ=0