84. (Third problem of Cluster)
(a) With the series pair C
2
and C
3
reduced to a single C
= 10 µF capacitor, this becomes verysimilar
to problem 82. Noting for later use that q
= q
2
= q
3
, and using notation similar to that used in
the solution to problem 82, we have
Q = q
1
+ q
where Q = C
1
V
bat
= 400 µC. Also, after switch S is closed,
V
1
=
V
q
1
C
1
=
q
C
which yields
1
4
q
1
= q
. Therefore,
Q = q
1
+
1
4
q
1
which gives the result q
1
= 320 µC.
(b) We use q
2
= q
3
=
1
4
q
1
to obtain the result 80 µC.
(c) See part (b).
(d) (e) and (f) Eq. 26-1 yields
V =
q
C
=
8.0 V
for C
1
5.3 V
for C
2
2.7 V
for C
3