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73
where I
o
exhibits resonance behaviour . The amplitude I
o
is given by
2
1
2
2
0
0
C
L
1
L
R
I
±
²
³
³
´
µ
¶
¶
·
¸
¹
¹
º
»

+
=
ω
ε
(4)
R
C
1
L
Tan
α

=
(5)
Gives the phase of the current relative to the applied emf. We can write I
o
=
o
/
Z
where ,
2
1
2
2
C
1
L
R
Z
±
²
³
³
´
µ
¶
¶
·
¸
¹
¹
º
»

+
=
(6)
is the impedance of the circuit .The reactance X of the circuit is
L
1
L
X

=
,
(7)
so that the impedance Z is given by
Z= ( R
2
+ X
2
)
1/2
Clearly the impedance will be minimum (and I
o
will be maximum) at resonance
condition when the reactance vanishes, i.e.
. at the angular frequency (known as
resonance frequency )
C
L
1
0
=
(8)
which is the natural frequency of electromagnetic oscillations in LCR circuit without
an external source of emf .
I.2
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 Fall '09
 LIND

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