UNIT7 AC Circuits Ch 10 AC Circuits Next

UNIT-7 AC Circuits Ch. 10 AC Circuits Next

7. 1 Series RL Circuit : - In AC circuits, the two voltages must be added by treating them as phasors, 30������� 2020 Ch. 10 AC Circuits Next 2

How to Draw Phasor Diagram 1. Mark the source voltage V, with its polarity. Mark the source current I leaving the positive terminal. 2. Mark ‘the voltage across’ and ‘the current through’ each individual component of the circuit, following the passive sign convention. 3. Draw the phasor diagrams for individual components. 4. Superimpose all the individual phasor diagrams, by recognizing the common phasor among them. 5. For this, you may have to rotate some phasor diagrams. 6. Find the phasor addition by drawing the parallelogram. 30������� 2020 Ch. 10 AC Circuits Next 3

(b) Phasor diagram for R. (c) Phasor diagram for L. (d) Phasor diagram for L, rotated by +90°. 30������� 2020 Ch. 10 AC Circuits (e) The complete phasor diagram. Next 4

Complex Impedance n n Complex impedance = (resistance) + j (reactance) or Z = R + j. X For the series RL circuit, 30������� 2020 Ch. 10 AC Circuits Next 5

Impedance Triangle • We can separate the voltage triangle OAB. • Dividing each side of this triangle by I, we get an impedance triangle. • Note that an inductive circuit has an impedance triangle in the first quadrant of complex plane. 30������� 2020 Ch. 10 AC Circuits Next 6

n n Often, we are given the source voltage. We take voltage as reference and then find the resulting current. Click 30������� 2020 Ch. 10 AC Circuits Next 7

Example 1 For the series RL circuit shown, n Calculate the rms value of the steady state current and the relative phase angle. n Write the expression for the instantaneous current. n Find the average power dissipated in the circuit. n Determine the power factor. n Draw the phasor diagram. 30������� 2020 Ch. 10 AC Circuits Next 8

Solution : The applied voltage can be written as Click 30������� 2020 Ch. 10 AC Circuits Next 9

Click (a) Phasor diagram (with I as ref. ) 30������� 2020 (a) Phasor diagram (with V as ref. ) Ch. 10 AC Circuits Next 10

7. 2 Series RC Circuit : - (a) The circuit. Click (c) Impedance triangle. (b) Phasor diagram. 30������� 2020 Ch. 10 AC Circuits Next 11

Click By applying KVL, we get Since the voltage across a capacitor lags the current by 90°. • Note that –j is associated with XC (whereas +j is associated with XL). 30������� 2020 Ch. 10 AC Circuits Next 12

Complex Power Let the terminal voltage, and the current, The average power absorbed, By using Euler’s formula, the above equation 30������� 2020 Ch. 10 AC Circuits Next 13

We now define the complex power as Note : • The magnitude VI of S is the apparent power (VA). • The angle of S is the pf angle. • The real part P of S is the real power (W). • The imaginary part Q of S is reactive power (VAR), 30������� 2020 Ch. 10 AC Circuits Next 14

Example 2 n A current of 0. 9 A flows through a series combination of a resistor of 120 Ω and a capacitor of reactance 250 Ω. Find the impedance, power factor, supply voltage, voltage across resistor, voltage across capacitor, apparent power, active power and reactive power. 30������� 2020 Ch. 10 AC Circuits Next 15

Click Solution : Let Click Click 30������� 2020 Ch. 10 AC Circuits Next 16

7. 3 Parallel RL Circuit : - (a) The circuit. Click (b) Phasor diagram. Click 30������� 2020 Ch. 10 AC Circuits Next 17

Y is the complex admittance of the parallel RL circuit, For parallel RL circuit, 30������� 2020 Ch. 10 AC Circuits Next 18

7. 4 Parallel RC Circuit : - (a) The circuit. Click (b) Phasor diagram. Click 30������� 2020 Ch. 10 AC Circuits Next 19

The complex admittance, 30������� 2020 Ch. 10 AC Circuits Click Next 20

Example 3 n When a two-element parallel circuit is connected across an ac source of frequency 50 Hz, it offers an impedance Z = (10 – j 10) Ω. Determine the values of the two elements. Solution : The nature of the impedance indicates that the circuit is capacitive. We find the admittance of the circuit, 30������� 2020 Ch. 10 AC Circuits Next 21

Click 30������� 2020 Ch. 10 AC Circuits Next 22

7. 5 Series RLC Circuit: (a) The circuit. Click (b) Phasor diagram (when ωL > 1/ ωC) 30������� 2020 (c) Phasor diagram (when ωL< 1/ ωC). Ch. 10 AC Circuits Next 23

Click 30������� 2020 Ch. 10 AC Circuits Next 24

There can be following three possibilities : (1) When ωL > 1/ ωC : The circuit behaves as an inductive circuit. (2) When ωL < 1/ ωC : The circuit behaves as a capacitive circuit. (3) When ωL = 1/ ωC : The circuit behaves as a purely resistive circuit. This is a special case, and is called resonance. 30������� 2020 Ch. 10 AC Circuits Next 25

Example 4 n n For the circuit shown, calculate (a) the impedance, (b) the current, (c) the phase angle, (d) the voltage across each element, (e) the power factor, (f) the apparent power, and (g) the average power. Also, draw the phasor diagram. 30������� 2020 Ch. 10 AC Circuits Next 26

Click Solution : Click (a) The impedance, (b) The current, Click (c) The phase angle, 30������� 2020 Ch. 10 AC Circuits Next 27

(e) The power factor, (f) The apparent power, Click (g) The average power, Click Phasor Diagram 30������� 2020 Ch. 10 AC Circuits Next 28

Example 5 n n A 100 -٠resistor is connected in series with a choke coil. When a 440 -V, 50 -Hz ac voltage is applied to this combination, the voltage across the resistor and the choke coil are 200 V and 300 V, respectively. Find the power consumed by the choke coil. Sketch a neat phasor diagram, indicating the current and all voltages. 30������� 2020 Ch. 10 AC Circuits Next 29

Solution : • A choke coil has some resistance, say r, and some inductance, say L. • Because of this resistance r, the voltage VCh leads the current I by an angle less than 90° (say, angle θ). • Hence, V = VR + VCh. 30������� 2020 Ch. 10 AC Circuits Next 30

Click Now, Click 30������� 2020 Ch. 10 AC Circuits Next 31

7. 6 Parallel RLC Circuit : - (a) The circuit. (b) Phasor diagram. Click or 30������� 2020 Ch. 10 AC Circuits Next 32

Obviously, Note that +j is associated with YC (and not with XL) and –j with YL. 30������� 2020 Ch. 10 AC Circuits Next 33