Series parallel ac networks

Series-Parallel ac networks:

Impedance and Phasor diagram

Series-Parallel ac networks: Impedance and Phasor diagramResistive elementsFor the purely resistive circuit, the voltage and Current are in phase and the magnitude is

In phasor form where

Applying Ohm’s law

since v and I are in phase

In time domain

V = 0.707 Vm

Series-Parallel ac networks: Impedance and Phasor diagram

Resistive elementsIn polar form the phase relationship between the voltage and the current of a resistor is

•

Phasor: A radius vector having a constant magnitude is called a phasor, when applied to electric circuit.

Phasor diagram shows at a glance the magnitude and phase relations among the various quantities with in the network

• ZR is referred to as the impedance of a resistive element

• Impedance is a measure of how much the element will impede the flow of charge through the network

• ZR has both magnitude and an associated angle ZR is measured in ohms

AC Fundamentals : Power in AC circuits

Ex: Using complex algebra, find the current i for the circuit of Fig. Sketch the waveforms of v and i.

Waveforms of voltage and current and phasor diagram are shown in Fig

AC Fundamentals : Power in AC circuits

Ex: Using complex algebra, find the current v for the circuit of Fig. Sketch the waveforms of v and i.

Waveforms of voltage and current and phasor diagram are shown in Fig

Series-Parallel ac networks: Impedance and Phasor diagramInductive ReactanceFor a pure inductor, the voltage leads the current by 90, and the reactance of the coil XL is determined by L.


Since v leads i by 90, i must have an angle of - 90 associated with it. L=+90

Therefore

In time domain

V = 0.707 Vm


Inductive Reactance

In polar form inductive reactance, which is the phase relationship between the voltage and the current of an inductor is

• ZL is known as the impedance of a inductive element• ZL has both magnitude and an associated angle• It is measured in ohms. • Inductive reactance is a measure of how much the element will control or impede the level of current through the network.


Ex: Using complex algebra, find the current i for the circuit of Fig. Sketch the waveforms of v and i


Ex: Using complex algebra, find the current v for the circuit of Fig. Sketch the waveforms of v and i


Series-Parallel ac networks: Impedance and Phasor diagramCapacitive ReactanceFor a pure capacitor of Fig. the currentleads the voltage by 90 and the reactanceof the capacitor XC is determined by 1/C.


Since i leads v by 90, i must have an angle of + 90 associated with it. C=-90

Therefore

In time domain

V = 0.707 Vm

Series-Parallel ac networks: Impedance and Phasor diagramCapacitive ReactanceFor a pure capacitor of Fig. the currentleads the voltage by 90 and the reactanceof the capacitor XC is determined by 1/C.


Since i leads v by 90, i must have an angle of + 90 associated with it. C=-90

Therefore

In time domain

V = 0.707 Vm


Capacitive Reactance

In polar form capacitive reactance, which is the phase relationship between the voltage and the current of a capacitor is

• • ZC is known as the impedance of a capacitive element. • ZC having both magnitude and an associated angle• It is measured in ohms. • Capacitive reactance is a measure of how much the element will control or impede the level of current through the network.


Capacitive Reactance

In polar form capacitive reactance, which is the phase relationship between the voltage and the current of a capacitor is

• • ZC is known as the impedance of a capacitive element. • ZC having both magnitude and an associated angle• It is measured in ohms. • Capacitive reactance is a measure of how much the element will control or impede the level of current through the network.


Ex: Using complex algebra, find the current i for the circuit of Fig. Sketch the waveforms of v and i


Ex: Using complex algebra, find the current v for the circuit of Fig. Sketch the waveforms of v and i

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Series parallel ac networks