what is parallel combination✍✍☹️
Answers
Answer:
Table of Contents:
Capacitor, Types and Capacitance
Combination of Capacitors
Energy Stored in a Capacitor
How Capacitors are connected?
Capacitors combination can be made in many ways. The combination is connected to a battery to apply a potential difference (V) and charge the plates (Q). We can define the equivalent capacitance of the combination between two points to be
C=\frac{Q}{V}C=
V
Q
Two frequently used methods of combination are: Parallel combination and Series combination
Parallel Combination of Capacitors
When capacitors are connected in parallel, the potential difference V across each is the same and the charge on C1, C2 is different i.e., Q1 and Q2.
Parallel combination of Capacitors
The total charge is Q given as:
Q={{Q}_{1}}+{{Q}_{2}}Q=Q
1
+Q
2
Q={{C}_{1}}V+{{C}_{2}}VQ=C
1
V+C
2
V \frac{Q}{V}={{C}_{1}}+{{C}_{2}}
V
Q
=C
1
+C
2
Equivalent capacitance between a and b is:
C = C1 + C2
The charges on capacitors is given as:
Q1=\frac{{{C}_{1}}}{{{C}_{1}}+{{C}_{2}}}QQ1=
C
1
+C
2
C
1
Q
Q2=\frac{{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}QQ2=
C
1
+C
2
C
2
Q
In case of more than two capacitors, C = C1 + C2 + C3 + C4 + C5 + …………
Watch this Video for More Reference
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Series Combination of Capacitors
When capacitors are connected in series, the magnitude of charge Q on each capacitor is same. The potential difference across C1 and C2 is different i.e., V1 and V2.
Series Combination of Capacitors
Q = C1 V1 = C2 V2
The total potential difference across combination is:
V = V1 + V2
V=\frac{Q}{{{C}_{1}}}+\frac{Q}{{{C}_{2}}}V=
C
1
Q
+
C
2
Q
\frac{V}{Q}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}
Q
V
=
C
1
1
+
C
2
1
The ratio Q/V is called as the equivalent capacitance C between point a and b.
The equivalent capacitance C is given by: \frac{1}{C}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}
C
1
=
C
1
1
+
C
2
1
The potential difference across C1 and C2 is V1 and V2 respectively, given as follows:
{{V}_{1}}=\frac{{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}};\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{V}_{2}}=\frac{{{C}_{1}}}{{{C}_{1}}+{{C}_{2}}}VV
1
=
C
1
+C
2
C
2
;V
2
=
C
1
+C
2
C
1
V
In case of more than two capacitors, the relation is:
\frac{1}{C}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}+\frac{1}{{{C}_{3}}}+\frac{1}{{{C}_{4}}}+……
C
1
=
C
1
1
+
C
2
1
+
C
3
1
+
C
4
1
+……
Important Points:
If N identical capacitors of capacitance C are connected in series, then effective capacitance = C/N
If N identical capacitors of capacitance C are connected in parallel, then effective capacitance = CN
Problems on Combination of Capacitors
Problem 1: Two capacitors of capacitance C1 = 6 μ F and C2 = 3 μ F are connected in series across a cell of emf 18 V. Calculate:
The equivalent capacitance
The potential difference across each capacitor
The charge on each capacitor
Sol:
(a) \frac{1}{C}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}
C
1
=
C
1
1
+
C
2
1
\Rightarrow C = \frac{{{C}_{1}}{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}=\frac{6\times 3}{6+3}=2\mu F⇒C=
C
1
+C
2
C
1
C
2
=
6+3
6×3
=2μF
(b) {{V}_{1}}=\frac{C{}_{2}}{{{C}_{1}}+{{C}_{2}}}V=\frac{3}{6+3}\times 18=6\,voltsV
1
=
C
1
+C
2
C
2
V=
6+3
3
×18=6volts
{{V}_{2}}=\frac{C{}_{1}}{{{C}_{1}}+{{C}_{2}}}V=\frac{6}{6+3}\times 18=12\,voltsV
2
=
C
1
+C
2
C
1
V=
6+3
6
×18=12volts
(c) Q1 = Q2 = C1 V1 = C2 V2 = CV
Charge on each capacitor = Ceq V = 2μF x 18 volts = 36μC
In the above problem, note that the smallest capacitor has the largest potential difference across it.
Example 2: Find the equivalent capacitance between points A and B capacitance of each capacitor is 2 μF.
Sol: In the system given, 1 and 3 are in parallel. 5 is connected between A and B. So, they can also be represented as follows.
As 1 and 3 are in parallel, their effective capacitance is 4μF
4μF and 2μF are in series, their effective capacitance is 4/3μF
4/3μF and 2 μF are in parallel, their effective capacitance is 10/3μF
10/3μF and 2μF are in series, their effective capacitance is 5/4μF
5/4μF and 2μF are in parallel, their effective capacitance is 13/4μF
Therefore the equivalent capacitance of the given system is 13/4μF.
Explanation:
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Explanation:
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