and the phase of . Show that 
. Find the impedence Z for this
circuit.
Answer:
In Fig. 4(EP).32, let 
be the total current from the
source. It is divided into two parts : 
through
R and 
through series combination of
C and L, such that 
As 
??(i)
If 
is charge on C at time t, then
for series combination of C and L,
??.(ii)
Let
??.(iii)
and
Putting
in (ii), we get
If 
??..(iv)
From
(iii), 
using
(iv), 
Taking
??(v)
From (i) and (v), we find that and
are out of phase.
Now, 
Put
and 
where
and 
and
Hence, 
or 
This
is the expression for impedance Z of the circuit.
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