21
Fundamentals of Electric Capacitors
1.6 C apacitor Containing Electrical Circuits
and Corresponding Calculation
In general, all electric circuits are driven by an external power source such
as a portable battery, supercapacitor, stationary electric generator, solar cell,
or thermopile. Despite their distinct modes of operation, they all have the
same principal function: performing work on charge carriers while keeping
a potential difference between their connected terminals.
1.6.1 Circuit Resistors
For a single loop circuit with a passive resistance element R connected to an
external power source with a voltage of V 0 , the sum of the potentials within
this loop should equate to zero according to Kerchoff’s voltage law:
V 0 – IR = 0
(1.33)
From Equation (1.33), the current flow through the resistor
V
0
I =
R
and the corresponding power I 2 R can be obtained. Series resistances in a
single loop experience an identical current passing through them. By applying Kerchoff’s voltage law, the sum of the series resistances can be equated to
a single equivalent resistance R eq . In contrast, resistances in parallel experience the same potential derived from the external power source, and a reciprocal R eq is equal to the sum of the reciprocal resistances.
1.6.2 Circuit Capacitors
Figure 1.8a and Figure 1.8b show an arrangement of capacitor elements in
series and/or parallel within a single-loop circuit. For simplifying the circuit, a replacement equivalent capacitor can be considered to have the same
capacitance as that of all the actual capacitors combined. If the capacitors
are arranged in parallel to an applied potential V o , each of them will experience the same equivalent potential difference V o . The charge in each individual capacitor can be expressed as the following, according to Equation
(1.11):
Q 1 = C 1 V o ; Q 2 = C 2 V o ; Q 3 = C 3 V o ; etc.
(1.34)
The total charge of the combination can then be calculated as