Bukhovtsev-et-al-Problems-in-Elementary-Physics

310 ANSWERS AND SOLUTIONS
+/l
U
-1/
~u
+1/-1/ -1/+1/
8 r:
C
(b) (c) Fig. 425
When the capacitor C 2 is short-circuited, the charge -q is neutralized.
The potential difference between the plates of the capacitor C should remain
approximately equal to U, since q ~ Q. The work required to move the charge
along the circuit ABCDA is zero. Therefore, the voltage across the capacitor
C t should become equal to ~ U and the charges on it to +2q and
-2q. The charges on the plates of the capacitor C will be +Q -q and
- Q + q, respectively (Fig. 425b).
When the capacitor C is disconnected from the earth, the distribution of
the charges and, hence, of the potentials will not change.
If the capacitor C 1 is shorted, the charges will be redistributed as shown
in Fig. 425c. It is only in this case that the required potentials relative to
the earth will be obtained: zero on the left plate and ~ U on the right
one. When the plates are earthed alternately, the potential difference between
the plates will gradua lly drop because the charge decreases.
440. No, they will not. When the plates are alternately earthed the same
processes will take place as in the absence of the battery (see Problem 439).
The only difference is that the potential difference between the plates is
always kept constant.
441. The total energy of the two capacitors before connection is
1 (~ 2)
Weo= 2 CIU1+C2U~
and after connection
W _..!..~_..!..(CIUl+C2U2)2
er: 2 C 1+C2
- 2 C1+C 9
It is easy to see that Weo> We. The difference in the energies is
Weo-We=c~f~s (U~+U:-2U1U2) > 0
When U 1=U2 , we have W eo - We=O, and when C 1=C2 and U 2=O, then
Weo=2We·
The electrostatic energy diminishes because when the capacitors are connected
by conductors, the charges flow from one capacitor to the other. Heat
is liberated in the connecting conductors. The quantity of heat evolved will
not depend on the resistance of the conductors. When the resistance is low,
the conductors will allow greater currents to flow through them, and vice
versa.