A
capacitor
is a component used for storing electrical charge, and usually consists
of two plates or sheets of conductor placed very close to (but not
touching) each other. As the capacitor charges up, one of these
conductors becomes positively charged while the other one becomes
negatively charged.
Capacitance
(C) is defined as the ratio of the charge (Q) stored in a capacitor to
the voltage (V) across the capacitor. Mathematically, therefore, C =
Q/V. The unit
of measurement for capacitance is the 'farad', F, which is defined as
coulomb/volt (coulomb and volt are the units of measurement for charge
and voltage, respectively). The higher
the capacitance of a capacitor, the greater is the charge it can store
for a given voltage across it.
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Figure 1. Photo of Capacitors |
Capacitors
may be connected to each other to form new values of capacitance. They
may be connected in series or in parallel, as shown in Figure 2.
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Figure 2. Capacitors in parallel (left) and in
series (right) |
When N
capacitances are connected in
series and a
voltage V is applied across them, V = V1 + V2 + ... + VN = Q1/C1 + Q2/C2
+ ... + QN/CN, where Qi
and Vi are the corresponding charge in and voltage across every
individual capacitance Ci, respectively. However, Q1 = Q2 =
... = QN, since each capacitor in the series experiences the same
current or flow of charge. From earlier equations, Q/Ceff = Q/C1 +
Q/C2 + ... + Q/CN.
This equation
may be simplified as follows: 1/Ceff =
1/C1 + 1/C2 + ... + 1/CN.
Thus, the
reciprocal of the effective capacitance of N capacitors connected in series is
equal to the sum of the reciprocals of their individual capacitances,
i.e.,
1/Ceff = 1/C1 + 1/C2 + ... + 1/CN.
When two or
more capacitors are connected in
parallel,
the voltages across each of them are equal. However, the
corresponding charge accumulated in each of them differs in accordance
with the equation Q = CV. Thus, for a given circuit
consisting of N capacitors connected in parallel and excited by a voltage
V, V = Q1/C1 = Q2/C2 = ... = QN/CN, where where Qi
and Vi are the corresponding charge in and voltage across every
individual capacitance Ci, respectively.
The total
amount charge Q accumulated by all the capacitors is equal to the sum of
the individual charges accumulated by the individual capacitances, or Q
= Q1 + Q2 + ... + QN, which may be rewritten as CeffV = C1V + C2V +
... + CNV, since the voltage across all the capacitors is V. This
equation may be simplified as follows: Ceff =
C1 + C2 + ... + CN.
Thus, the
effective capacitance of N capacitors connected in parallel is
just the sum of their individual capacitances, i.e., Ceff = C1 + C2 +
... + CN.
See Also:
Capacitance Equations;
Resistance;
Self-Inductance
