Solutions 277The total energy of the system after recharging is
q; 2W2 = 2Cq a +2C 2 2 (CI+ C 2 )The amount of heat liberated in the resistor during
this time is(10R)2C2Q=w1—w2 (^) 2 (Ci + C 2 )
3.46. Before switching the key K, no current flows
through the resistor of resistance R, and the charge
on the capacitor of capacitance C2 can be deter-
mined from the formula
q =--- WC2.
The energy stored in this capacitor is found from
the formula
2 C2
WC2 = 2
After switching the key K, the charge q is re-
distributed between two capacitors so that the
charge q 1 on the capacitor of capacitance C 1 and
the charge q 2 on the capacitor of capacitance C2
can be calculated from the formulas
ql+ q2 = q, q2
CI (^) C2
The total energy of the two capacitors will be
q (^2) g2cd
WC, (^) 2 (C 2 + C 2 ) — 2 (C2-F C2)
Therefore, the amount of heat Q liberated in the
resistor can be obtained from the relation
YE 2 C 2 2 C 2 C2^ % (^2) C1C2
Q=
2 2 C 1 + C2 = 2 (C1+ C2)
3.47. By the moment when the voltage across the
capacitor has become U, the charge q has passed