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Electrical Energy and Capacitance
61
16.54
For the parallel combination:
CC
1
p
C
2
=
+
which gives
(1)
For the series combination:
2
p
CCC
=−
1
1
1
1
s
C
C
−
=
12
111
=+
2
or
ss
s
Thus, we have
1
s
2
1
s
C
=
−
and equating this to Equation (1) above gives
1
1
1
s
p
s
−=
−
or
2
11
s
s
C
+
1
pp
−−
1
s
=
We write this result as :
2
0
s
C
−
+=
and use the quadratic formula to obtain
2
1
24
p
s
C
C
C
=±
−
Then, Equation (1) gives
2
2
p
s
C
C
C
∓
16.55
The charge stored on the capacitor by the battery is
( ) ( )
1
100 V
QC V
C
=∆ =
This is also the total charge stored in the parallel combination when this charged
capacitor is connected in parallel with an uncharged 10.0- F
µ
capacitor. Thus, if
( )
2
V
∆
is
the resulting voltage across the parallel combination,
( )
2
V
p
QC
=
∆
gives
( ) ( )( )

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