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
( ) ( )( )
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 STAFF
 Physics, Capacitance, Energy, Quadratic equation, Electric charge, Inductor

Click to edit the document details