الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

Capacitors and capacitance
4.5 Energy stored in a charged capacitor (in electric field)
If the capacitor is connected to a power supply such as battery, charge will
be transferred from the battery to the plates of the capacitor. This is a
charging process of the capacitor which mean that the battery perform a
work to store energy between the plates of the capacitor.
Consider uncharged capacitor is connected to a battery as shown in figure
6.8, at start the potential across the plates is zero and the charge is zero as
well.
C
S
V
Figure 6.8
If the switch S is closed then the charging process will start and the potential
across the capacitor will rise to reach the value equal the potential of the
battery V in time t (called charging time).
بعد إغلاق المفتح S
مساويا ً لفرق جهد البطارية.‏
تستمر عملية شحن المكثف حتى يصبح فرق الجهد بين لوحي المكثف
Suppose that at a time t a charge q(t) has been transferred from the battery
to capacitor. The potential difference V(t) across the capacitor will be
q(t)/C. For the battery to transferred another amount of charge dq it will
perform a work dW
q
dW = Vdq = dq (6.11)
C
The total work required to put a total charge Q on the capacitor is
2
Q q Q
W = ∫ dW = ∫ dq =
(6.12)
0
C 2C
Using the equation q=CV
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