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Unformatted text preview: citances are also equal,
so by V = Q/C they each have the same potential difference. Their potentials must sum to 140 V, so the potential
across each is 47 V and Vcd # 47 V.
EVALUATE:! In each capacitor network the rules for combining V for capacitors in series and parallel are obeyed.
Note that Vcd 1 V , in fact V ! 2(140 V) ! 2(47 V) # Vcd .
IDENTIFY:! Find the total charge on the capacitor network when it is connected to the battery. This is the amount of
charge that flows through the signal device when the switch is closed.
SET UP:! For capacitors in parallel, Ceq # C1 0 C2 0 C3 0 %
EXECUTE:! Cequiv # C1 0 C2 0 C3 # 60.0 $ F . Q # CV # (60.0 $ F)(120 V) # 7200 $ C . 24.65. EVALUATE:! More charge is stored by the three capacitors in parallel than would be stored in each capacitor used
alone.
(a) IDENTIFY and SET UP:! Q is constant. C # KC0 ; use Eq.(24.1) to relate the dielectric constant K to the ratio of
the voltages without and with the dielectric.
EXECUTE:! With the dielectric: V # Q / C # Q / . KC0 / without the dielectric: V0 # Q / C0
V0 / V # K , so K # . 45.0 V / / .11.5 V / # 3.91
EVALUATE:! Our analysis agrees with Eq.(24.13).
(b) IDENTIFY:! The capacitor can be treated as equivalent to two capacitors C1 and C2 in parallel, one with
area 2A/3 and air between the plates and one with area A/3 and dielectric between the plates.
SET UP:! The equivalent network is shown in Figure 24.65. Figure 24.65
EXECUTE:! Let C0 # !0 A / d be the capacitance with only air between the plates. C1 # KC0 / 3, C2 # 2C0 / 3; Ceq # C1 0 C2 # (C0 / 3)( K 0 2)
V# Q
Q% 3 &
%3&
%3&
#'
( # V0 '
( # . 45.0 V / '
( # 22.8 V
Ceq C0 ) K 0 2 *
K 02*
)
) 5.91 * EVALUATE:! The voltage is reduced by the dielectric. The voltage reduction is less when the dielectric doesn’t
completely fill the volume between the plates. Capacitance and Dielectrics 24.66. IDENTIFY:! This situation is analogous to having two capacitors C1 in series, each with separation 1
2 2421 (d ! a ). 1
1
1
#0
.
SET UP:! For capacitors in series,
Ceq C1 C2
!1 24.67. !0 A
!A
%
&
EXECUTE:! (a) C #...
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This document was uploaded on 03/11/2014 for the course PHYSICS 240 at University of Michigan.
 Fall '08
 DaveWinn
 Physics

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