21'3 RCL circuit

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21.3 RCL circuit

• RLC circuit
• Resonance
• transformer

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RLC circuit
Currents and voltages are sinusoidal Charge and
discharge of capacitor Energy only dissipated in
R At resonance frequency maximum energy stored
in electric and magnetic fields. This circuit
can be used to pick out selected frequencies.
e.g. in a radio receiver.
-

3
RLC circuit
Currents and voltages are sinusoidal Charge and
discharge of capacitor Energy only dissipated in
R At resonance frequency maximum energy stored
in electric and magnetic fields. This circuit
can be used to pick out selected frequencies.
e.g. in a radio receiver.

-
4
Voltages
Voltage across R ,L , C are sinusoidal But with
different phase relative to the current, and
relative to each other The sum of voltage drops
?Vs ? VR ? VL ? VC is true at
any time
The sum of sine waves with constant f is also a
sine wave.
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Sum of Voltages
I
t
?VR
?VL
IImaxsin2pft
?VC
?V ?VR ?VL ?VC
?V?Vmaxsin(2pftFi)
?V
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Phasors
Representation of a sine wave
?Vmax
?V
t
phasor vector with constant amplitude ?Vmax
rotating with constant frequency ?2pftF
?Vmax
?
?V
y component of rotating phasor
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Phasor addition of ?VR, ?VL, ?VC
at t0
?VR
?V
?VL
?VL
?VR
?VC
?VC
?V
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Impedence, Z
Like Ohms Law
L, C and R contribute to Z but not a additive
fashion
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Example 21.4 For a series RLC circuit with R250
O, L 0.6 H,C3.5 µF, f60 Hz, Vmax150 V, Find
Imax and F.
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Resonance
XL and XC are functions of f at some f, XL
XC then XL-XC0 Z becomes a minimum I becomes
maximum
resonance frequency
R0 Iinfinity at resonance
I
Rgt0
f
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34. A resonance circuit in a radio receiver is
tuned to a certain station when the inductor has
a value of 0.20 mH and the capacitor has a value
of 30 pF. Find the frequency of the station.
antenna
resonance circuit
amplifier
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For LC circuit (R-gt0) Energy oscillates between
Electric and Magnetic Fields

-
Emax
Bmax
Emax
Bmax
I
t-gt
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Transformer
Iron core
N1
N2
primary
secondary
Ideal transformer
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Step up transformer
N2 gtN1
?V2 gt ?V1
I2 lt I1
Step down transformer
?V1
N2 lt N1 ?V2 lt ?V1 I2 gt I1
?V2
R
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A transformer has 800 turns in the primary and 60
turns in the secondary. If the input voltage has
a frequency of 60 Hz, V 120 V, I 0.02 A, find
the voltage and current at the secondary.
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Applications of Transformers Electrical power
transmission lines. Power supplies.
Electronic equipment low voltage DC
step-up transformer