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3.Capacitors (1)

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Capacitor
Capacitors are devices that store electric charge. The charge is released at a later time when it is
needed.
Capacitors when not mounted on an
electronic board.
Capacitance
• A capacitor consist of two conductors of any shape, placed near, but not touching
one another. Often the space between the conductors is filled with an electrically
insulating material.
• Each plate carries a charge of the same magnitude, one being positive, while the
other is negative.
• The charge that is stored on the plates of a capacitor is proportional to the potential
difference across the plates. Thus
where is proportionality constant called capacitance. The capacitance is defined as
an ability of the capacitor to store an electrical charge. The unit of capacitance is the
farad (1 F = 1 CV-1). One farad is a very large unit and in practice, capacitances are
normally much less than this. Some common capacitances are:
+
Battery
Capacitor
Capacitors in series
οƒ˜ Capacitors in series all carry the same charge which is equal to the charge on π‘’π‘ž .
οƒ˜ The sum of the potential difference across each capacitor is equal to the potential difference across
From
π‘ž
π‘ž
π‘ž
π‘ž
+ +
=
𝐢
𝐢
𝐢
𝐢
𝒆𝒒.
Capacitors in parallel
q1
q2
q3
V
q
V
V
οƒ˜ The voltage across each capacitor is the same, which is also equal to the voltage across the equivalent
capacitance.
οƒ˜ The charge in each capacitor is not the same i.e.
οƒ˜ However, the total charge on all the individual capacitors is the same as the charge that would be stored on
a single equivalent capacitor i.e.
but
then
Energy stored in a Capacitor
Charging a capacitor requires energy. The work done in completely charging a capacitor
where
is the average voltage across the plates during charging. If the final voltage is
is given by
then
and the work done is
which is stored as electric potential energy in the capacitor. Since
.
the energy stored is
Capacitor and equivalent capacitance
Example 1.9: The equivalent capacitance of a combination of capacitors
For the arrangement shown alongside, calculate
(a) the single equivalent capacitance,
C1 = 10 μF
(b) the p.d. across the 10 μF capacitor,
(c) the energy stored in the 2 μF capacitor.
(a) 𝐢 = 𝐢 + 𝐢 = 2 + 3 = 5 πœ‡πΉ
1
1
1
+
=
𝐢
𝐢
𝐢
1 1
1
3
+ =
=
10 5 𝐢
10
1
3
=
𝐢
10
10
𝐢
=
= 3.33 πœ‡πΉ
3
(b) π‘ž
= 𝐢 𝑉 = 3.33 × 10 × 100
π‘ž
= 3.33 × 10 𝐢
π‘ž
= π‘ž = π‘ž so π‘ž =3.33 × 10 𝐢
π‘ž
3.33 × 10
∴𝑉 =
=
= 33.3 𝑉
𝐢
10 × 10
C2 = 2 μF
C3 = 3 μF
V = 100 V
(c) 𝑉 + 𝑉 = 100
𝑉 = 100 − 𝑉 = 100 − 33.3 = 66.7 𝑉
𝑉 = 𝑉 = 𝑉 = 66.7 𝑉
∴π‘Š = 𝐢 𝑉
π‘Š = × 2 × 10 × 66.7
π‘Š = 4.45 × 10 𝐽
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