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# Lesson 19 Impedance - PowerPoint PPT Presentation

Lesson 19 Impedance. Learning Objectives. For purely resistive, inductive and capacitive elements define the voltage and current phase differences. Define inductive reactance. Understand the variation of inductive reactance as a function of frequency. Define capacitive reactance.

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### Lesson 19Impedance

• For purely resistive, inductive and capacitive elements define the voltage and current phase differences.

• Define inductive reactance.

• Understand the variation of inductive reactance as a function of frequency.

• Define capacitive reactance.

• Understand the variation of capacitive reactance as a function of frequency.

• Define impedance.

• Graph impedances of purely resistive, inductive and capacitive elements as a function of phase.

R, L and C circuits with Sinusoidal Excitation

• R, L, C have very different voltage-current relationships

• Sinusoidal (ac) sources are a special case

• Impedance (Z) is the opposition that a circuit element presents to current in the phasor domain. It is defined

• Ohm’s law for ac circuits

X

q

R

Impedance

• Impedance is a complex quantity that can be made up of resistance (real part) and reactance (imaginary part).

• Unit of impedance is ohms ().

• For a purely resistive circuit, current and voltage are in phase.

• For resistors, voltage and current are in phase.

Two resistors R1=10 kΩ and R2=12.5 kΩ are in series.

If i(t) = 14.7 sin (ωt + 39˚) mA

• Compute VR1 and VR2

• Compute VT=VR1 + VR2

• Calculate ZT

• Compare VT to the results of VT=IZT

• Voltage-Current relationship for an inductor

• It should be noted that for a purely inductive circuit voltage leads current by 90º.

• Impedance can be written as a complex number (in rectangular or polar form):

• Since an ideal inductor has no real resistive component, this means the reactance of an inductor is the pure imaginary part:

• Voltage leads current by 90˚

• For inductors, voltage leads current by 90º.

• Solution technique

• Transform time domain currents and voltages into phasors

• Calculate impedances for circuit elements

• Perform all calculations using complex math

• Transform resulting phasors back to time domain (if reqd)

For the inductive circuit:

vL = 40 sin (ωt + 30˚) V

f = 26.53 kHz

L = 2 mH

Determine VL and IL

Graph vL and iL

vL = 40 sin (ωt + 30˚) V

iL = 120 sin (ωt - 60˚) mA

iL

Notice 90°phase difference!

vL

For the inductive circuit:

vL = 40 sin (ωt + Ө) V

iL = 250 sin (ωt + 40˚) μA

f = 500 kHz

What is L and Ө?

• Current-voltage relationship for an capacitor

• It should be noted that, for a purely capacitive circuit current leads voltage by 90º.

Impedance can be written as a complex number (in rectangular or polar form):

• Since a capacitor has no real resistive component, this means the reactance of a capacitor is the pure imaginary part:

• For capacitors, voltage lags current by 90º.

For the capacitive circuit:

vC = 3.6 sin (ωt-50°) V

f = 12 kHz

C=1.29 uF

Determine VC and IC

For the capacitive circuit:

vC = 362 sin (ωt - 33˚) V

iC = 94 sin (ωt + 57˚) mA

C = 2.2 μF

Determine the frequency

ELI the ICE man

Current

Current

Voltage

Voltage

Inductance

Capacitance