P26_067.PDF

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Chapter 26 - 26.67
67. (a) The equivalent capacitance is C eq = C 1 C 2 / ( C 1 + C 2 ) . Thus the charge q on each capacitor is
q = C eq V = C 1 C 2 V
C 1 + C 2 = (2 . 0 µ F)(8 . 0 µ F)(300 V)
2 . 0 µ F+8 . 0 µ F
=4 . 8
×
10 4 C .
The potential differences are: V 1 = q/C 1 =4 . 8
×
10 4 C / 2 . 0 µ F = 240 V, V 2 = V
V 1 = 300 V
240 V = 60 V .
(b) Now we have q 1 /C 1 = q 2 /C 2 = V ( V being the new potential difference across each capacitor)
and q 1 + q 2 =2 q .Wesolvefor q 1 , q 2 and V :
q 1 =
C 1 + C 2 = 2(2 . 0 µ F)(4 . 8
10 4 C)
2 . 0 µ F+8 . 0 µ F
×
=1 . 9
×
10 4 C ,
q 2 =2 q
q 1 =7 . 7
×
10 4 C ,
V =
C 1 = 1 . 92
10 4 C
2 . 0 µ F
×
=96V .
(c) In this circumstance, the capacitors will simply discharge themselves, leaving q 1 = q 2 =0and
V 1 = V 2 =0.
2 C 1 q
q 1
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