parallel circuits 2
DESCRIPTION
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ECR255
- 1 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 1
ECR255
Parallel AC Circuits
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ECR255
- 2 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 2
Find the Elements
Consider an unknown circuit in a box connected as shown
If total power P = 4 W with a leading power factor, what is
the simplest possible parallel circuit in the box if the
frequency is 1 kHz?
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ECR255
- 3 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 3
Find the Elements
P = E I cos θ
cos θ = P / E I = 4 W / 40 V x 150 mA = 0.6667
θ = 48.19o current leads voltage
I = 150 mA /48.19o
YT = I / E = 150 mA /48.19o / 40 V /0o = 3.75 mS /48.19o
= 2.50 mS + j 2.795 mS
= 1/ R + Gx + j Bx
Gx = 2.50 mS - 1.0 mS = 1.50 mS Rx = 667 Ω
Bx = 2.795 mS = 2π f Cx
Cx = Bx / 2π f = 2.795 mS / 2π x 103 = 445 nF3
P = 4 W leading - capacitivef = 1 kHz
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ECR255
- 4 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 4
Current Divider Rule
The basic format for the current divider rule in
ac circuits is exactly the same as that for dc
circuits; that is, for two parallel branches with
impedances Z1 and Z2 :
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ECR255
- 5 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 5
Example
Calculate the currents I1 I2 in phasor form using the current
divider rule
ZR = 22 Ω /0o
ZL = (XL1 + XL2) /90o = 80 Ω /90o
ZR + ZL = 22 Ω + j 80 Ω
ZR + ZL = 82.97 Ω /74.62o
I1 = I ZL / (ZR + ZL )
I1 = 20 A /40o x 80 Ω /90o / 82.97 Ω /74.62o = 19.3 A /55.38o
I2 = I ZR / (ZR + ZL )
I3 = 20 A /40o x 22 Ω /0o / 82.97 Ω /74.62o = 5.30 A /34.62o
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XL1
XL2
R
22 Ω
60 Ω
20 Ω
I2I1
I = 20 A /40o
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ECR255
- 6 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 6
Examples
For the circuit
a) Find the total admittance in polar form
b) Draw the admittance diagram
c) Calculate the capacitance and inductance of the devices
d) Find voltage E and currents IR IC IL in polar form
e) Draw phasor diagram of IS IR IC IL and E
f) Verify Kirchhoff’s current law at one node.
g) Find average power delivered to the load
h) Find power factor. Is it leading or lagging?
i) Find sinusoidal expressions for currents and voltage
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1.2 Ω
RX
L
XC
is
3 sin(377t+60o) 2 Ω 5 Ω
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ECR255
- 7 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 7
Frequency Response of Parallel Elements
As the frequency increases, XL will increase
until it equals the impedance of the resistor R.
For frequencies less than ƒ2: X
L< R. For
frequencies greater that ƒ2: X
L> R.
The magnitude and angle of the total
impedance can now be found at any
frequency of interest by substituting the
following equations:
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ECR255
- 8 – Seneca College – School of Information and Communications Technology G VandeBelt 112
Slide 8
Frequency Response of Parallel Elements
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