Physics---Capacitance 2

(a) With the like plates together, the charge amount is conserved since there's no neutralization occuring. Therefore,
Charge of the 10μF cap initially = 10 10-6 9 = 9 10-5 C
Charge of the 47μF cap initially = 47 10-6 6 = 2.82 10-4 C
So total charge = 3.72 10-4 C
Now, since they are connected together, they will have the same p.d., say V and hence:
(47 10-6 + 10 10-6) V = 3.72 10-4
V = 6.53 V
And the charges are:
10μF cap = 10 10-6 6.53 = 6.53 10-5 C

47μF cap = 47 10-6 6.53 = 3.07 10-4 C
(b) If the unlike plates are connected, neutralzation occurs and then net charge remained = 2.82 10-4 - 9 10-5 = 1.92 10-4 C
So using the same method as (a):

(47 10-6 + 10 10-6) V = 1.92 10-4
V = 3.37 V

And the charges are:
10μF cap = 10 10-6 3.37 = 3.37 10-5 C

47μF cap = 47 10-6 3.37 = 1.58 10-4 C


2008-02-28 14:57:03 補充：
Initial energy:
0.5 × (10^-5 × 9^2 + 4.7 × 10^-5 × 6^2) = 1.251 × 10^-3 J

(a) Final energy = 0.5 × (10^-5 × + 4.7 × 10^-5) × 6.53^2 = 1.215 × 10^-3 J
Energy dissipation = 3.573 × 10^-5 J

(b) Final energy = 0.5 × (10^-5 × + 4.7 × 10^-5) × 3.37^2 = 3.237 × 10^-4 J
Energy dissipation = 9.273 × 10^-4 J