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EEE107 AC Circuits 1.

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Presentation on theme: "EEE107 AC Circuits 1."— Presentation transcript:

1 EEE107 AC Circuits 1

2 Capacitance in AC Circuits
X Y Vc The current leads the voltage by 90o . The opposition to the flow of ac current in a capacitor is known as the capacitive reactance and is the equivalent of resistance in a resistor circuit. During the positive half-cycle of the voltage waveform, plate X of the capacitor becomes positively charged and plate Y negatively charged. During the negative half-cycle, X receives a negative charge and Y a positive one. There is therefore an alternating flow of charge or alternating current, i, through the capacitor Thus, unlike the case for a dc voltage where the capacitor eventually charges up to the value of the dc supply voltage and no more current flows, a capacitor continually conducts an ac current. Thus we may say that a capacitor passes ac and blocks dc. capacitive reactance is measured in Ohms. Note that it is inversely proportional to the frequency of the source.

3 Capacitor In a purely capacitive a.c. circuit the current IC leads the applied voltage VC by 900 In a purely capacitive a.c. circuit the opposition to current flow is known as Capacitive Reactance, XC Capacitive Reactance is measured in ohms

4 Capacitor Thus as frequency rises the capacitive reactance decreases non linearly reactance frequency

5 Capacitor In a purely capacitive a.c. circuit the current IC leads the applied voltage VC by 900

6 (Self ) Inductance A piece of wire wound in the form of a coil possesses an electrical property known as inductance. The property arises from the observable phenomenon that if a current flowing through the coil changes for some reason then an emf e is induced in the coil which tries to oppose the current change. The magnitude of the induced emf is proportional to the rate of change of current. The constant of proportionality is known as the inductance of the coil L and is measured in a unit called the henry. Mathematically we can summarise this with the equation

7 Inductance in AC Circuits
voltage or current IL (t) VL (t) vL iL The voltage leads the current by 90o . The opposition to the flow of ac current in an inductor is known as the inductive reactance and is the equivalent of resistance in a resistor circuit. Let inductive reactance is measured in Ohms. Note that it is proportional to the frequency of the source.

8 Inductor In a purely inductive a.c. circuit the current IL lags the applied voltage VL by 900

9 Inductor In a purely inductive a.c. circuit the current IL lags the applied voltage VL by 900 Circuit Diagram Phasor Diagram

10 Inductive Reactance is measured in ohms
Inductor In a purely inductive a.c. circuit the current IL lags the applied voltage VL by 900 In a purely inductive a.c. circuit the opposition to current flow is known as Inductive Reactance, XL Inductive Reactance is measured in ohms

11 Inductor Thus as frequency rises the inductive reactance increases linearily reactance frequency

12 Resistance and Inductance in series
As the current IS flows through both components it should be used as the reference for the phasor diagram

13 Resistance and Inductance in series
Circuit Diagram Phasor diagram Is the opposition to current flow in the circuit However as the current and voltage are not in phase this opposition to current flow is known as Impedance Z (Ω) As the current flowing lags the applied voltage the circuit is said to be inductively reactive

14 Resistance and Capacitance in series
As the current IS flows through both components it should be used as the reference for the phasor diagram

15 Resistance and Capacitance in series
Is the opposition to current flow in the circuit However as the current and voltage are not in phase this opposition to current flow is known as Impedance.(Z) (Ω) As the current flowing leads the applied voltage the circuit is said to be capacitively reactive

16 Voltage Triangle Phasor diagram for CR circuit
Voltage triangle for CR circuit If each of the voltages are divided by IS then opposition to current flow of each element is obtained.

17 Impedance Triangle Phasor diagram for CR circuit
Impedance triangle for CR circuit Using the same steps the voltage triangle and impedance triangle for R and L in series may be obtained

18 Impedance Triangle Phasor diagram for CR circuit
Impedance triangle for CR circuit

19 Find the inductive reactance XL
Find the Impedance Z Find the current flowing Find the voltage across the inductor Find the voltage across the resistor Phase angle between VS and IS

20 The point Z could be specified to the origin by :-

21 Construct a reactance/resistance/impedance vector for the above diagram

22 Construct a reactance/resistance/impedance vector for the above diagram

23 Note that as XC > XL the circuit Is said to be capacitively reactive
The series circuit could be replaced by a 20Ω resistor in series with a capacitive reactance of 5Ω


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