Certainly, I can help you with that! When capacitors are connected in parallel, their terminals are connected to the same two points. This configuration creates an equivalent capacitance that is the sum of the individual capacitances.
The formula for calculating the equivalent capacitance (
eq
C
eq
ā
) of capacitors connected in parallel is:
eq
=
1
+
2
+
3
+
ā¦
C
eq
ā
=C
1
ā
+C
2
ā
+C
3
ā
+ā¦
Where
1
C
1
ā
,
2
C
2
ā
,
3
C
3
ā
, etc., are the capacitances of the individual capacitors connected in parallel.
In other words, when you have
n capacitors connected in parallel, the equivalent capacitance is the sum of all the individual capacitances.
Here's a step-by-step explanation:
Start with
n capacitors with capacitances
1
C
1
ā
,
2
C
2
ā
,
3
C
3
ā
, up to
C
n
ā
.
Connect all the positive terminals of the capacitors together and all the negative terminals together.
The potential difference (
V) across all the capacitors will be the same, as they are connected to the same points.
The charge on each capacitor (
Q) is given by
=
ā
Q=Cā
V, where
C is the capacitance of the capacitor.
Since the potential difference across all the capacitors is the same, the total charge
eq
Q
eq
ā
on the parallel combination is the sum of the charges on individual capacitors:
eq
=
1
+
2
+
3
+
ā¦
Q
eq
ā
=Q
1
ā
+Q
2
ā
+Q
3
ā
+ā¦.
Substituting
=
ā
Q=Cā
V for each capacitor, you get
eq
=
1
ā
+
2
ā
+
3
ā
+
ā¦
Q
eq
ā
=C
1
ā
ā
V+C
2
ā
ā
V+C
3
ā
ā
V+ā¦.
Factor out
V, and you'll get
eq
=
ā
(
1
+
2
+
3
+
ā¦
)
Q
eq
ā
=Vā
(C
1
ā
+C
2
ā
+C
3
ā
+ā¦).
But
eq
Q
eq
ā
is also equal to the charge stored in the equivalent capacitor, so you have
eq
=
eq
ā
Q
eq
ā
=C
eq
ā
ā
V.
Equating the two expressions for
eq
Q
eq
ā
, you get
eq
ā
=
ā
(
1
+
2
+
3
+
ā¦
)
C
eq
ā
ā
V=Vā
(C
1
ā
+C
2
ā
+C
3
ā
+ā¦).
Finally, divide both sides by
V to get the formula for the equivalent capacitance:
eq
=
1
+
2
+
3
+
ā¦
C
eq
ā
=C
1
ā
+C
2
ā
+C
3
ā
+ā¦.
So, when capacitors are connected in parallel, the equivalent capacitance is simply the sum of the individual capacitances. This configuration increases the total charge storage capacity compared to a single capacitor, but the voltage across all the capacitors remains the same.