Example 17-11 Multiple Capacitors
Find the equivalent capacitance of the three capacitors shown in
Figure 17-16. The individual capacitances are C1 = 1.00 mF,
C2 = 2.00 mF, and C3 = 6.00 mF.
Set Up
Figure 17-16 ​A capacitor
network These three
capacitors are neither all in
series nor all in parallel.
Whenever capacitors are combined in ways
other than purely in series or purely in parallel, we look for groupings of capacitors that
are either in parallel or in series, and then we
combine the groups one at a time.
Two capacitors in series:
Notice in Figure 17-16 that C1 and C2 are
in parallel because their two right plates are
directly connected, as are their two left plates.
We can therefore use Equation 17-26 to find
C12 (the equivalent capacitance of the combination of C1 and C2) by using our relationship for
capacitors in parallel.
Capacitor C3 is in series with C12, so
we can find their combined capacitance by
using Equation 17-22. This result is C123, the
equivalent capacitance of all three capacitors.
Two capacitors in parallel:
Solve
First find the equivalent capacitance of the
parallel capacitors C1 and C2.
1
1
1
=
+
C equiv
C1
C2
Cequiv = C1 + C2
(17-22)
C1
C3
C2
Replace the parallel capacitors C1 and C2
by their equivalent capacitor C12:
C3
C12
Then find the equivalent capacitance of
C12 and C3 in series.
(17-26)
For C1 = 1.00 mF and C2 = 2.00 mF in parallel, the equivalent
­capacitance C12 is given by Equation 17-26:
C12 = C1 + C2 = 1.00 mF + 2.00 mF = 3.00 mF
Then find C123, the equivalent capacitance of
the series capacitors C12 and C3. This is the
equivalent capacitance of the entire network of
C1, C2, and C3.
Since C12 = 3.00 mF and C3 = 6.00 mF are in series, their equivalent
capacitance C123 is given by Equation 17-22:
1
1
1
1
1
=
+
=
+
C 123
C 12
C3
3.00 mF
6.00 mF
= 0.333 mF21 + 0.167 mF21 = 0.500 mF21
Take the reciprocal of this to find C123:
C 123 =
Reflect
1
= 2.00 mF
0.500 mF -1
As we described previously, when capacitors are connected in parallel, the equivalent capacitance is always greater
than the greatest individual capacitor. That’s why C12 is greater than either C1 or C2. When capacitors are connected
in series, the equivalent capacitance is always less than the least individual capacitor, which is why C123 is less than
either C12 or C3.