Review of AC-circuitKeys to deal with R, L, and C in an AC-circuit

• Across R, voltage and current are in-phase• Across L, the current lags behind voltage by 90o

• Across C, the current leads voltage by 90o

• When two elements are in series the same current passing through them

• When two elements are in parallel the same voltage across them

Also,

Basics I and V are in-phase

I lags V by 90 degree

I leads V by 90 degree

R

L

C

RLC in seriesKey: IR, IL, and IC are all in phase

VL ~ XL

VC ~ XC

VR ~ R

Vmax ~ Z

22 )( CL XXRZ

RXX CL1tan

What if RLC are not in series?Which of the following is true

(a) Vc = VL, IC = IL

(b) Vc = VL, IR = IL

(c) Vc = VR, IR = IL

(d) VL = VR, IR = IL

How do you draw the phasor diagram?

VL

VRIR = IL

IC

(e) Vc = VL+ VR, IC = IL

(f) Vc = VL+ VR, IR = IL

Imax Vc = VR+ VL

Power dissipation

• Only R dissipates power

P = I *V, alwaysFor L and C, I andV are 90o out of phase PL = 0, PC = 0

For R, I andV are in-phase PR = IV = Irms2R

Resonance in RLC circuit in series

22 )( CL XXRZ

RXX CL1tan

For a fixed AC voltage source, maximum power dissipation occurs when XL = XC, ie. When Z = R

PR = IV = Irms2R

Where Irms = Vrms/Z

LC1

i.e.