When positive electric charge on an isolated conducting sphere shown in figure 1 is gradually increased, electric potential on its surface and electric field in its vicinity increase. When the electric field becomes strong, it ionizes the surrounding air which causes charge on the sphere to leak and the charge on the sphere cannot be increased further. During this process, the ratio of charge ( Q ) and the electric potential ( V ) of the sphere remains constant. This ratio, Q / V, is called its capacitance ( C ). To increase capacitance C of the sphere, another isolated conducting sphere is brought near it on which charge is induced as shown in figure. 2. On earthing, the positive charge gets neutralized as shown in figure 3. 
The negative charge induced on the second sphere reduces the electric potential of the first sphere thereby increasing its charge storage capacity. The ratio Q / V of the charge on the first sphere and the potential difference between the two spheres is still constant and is called the capacitance C of the system. The value of C depends on the dimensions of the spheres, the distance between the two spheres and the medium between them. The arrangement in which two good conductors of arbitrary shape and volume, are arranged close to one another, but separated from each other, is called a capacitor. The conductors are known as plates of the capacitor. Positively charged conductor is called the positive plate and the negatively charged conductor the negative plate. Both the plates are equally charged. The charge on the positive plate is called the charge ( Q ) of the capacitor and taking the potential difference between the two plates as V, capacitance of the capacitor is C = Q / V. The S.I. unit of capacitance is coulomb / volt which is also called farad ( F ) named after the great scientist Michael Faraday. The smaller units of farad are microfarad ( m F = 10 (exp- 6) F ) and picofarad ( pF = 10 (exp-12) F ).
Parallel Plate Capacitor: -
This type of capacitor is made by two metallic plates having identical area and kept parallel to each other. The distance ( d ) between the two plates is kept less as compared to the dimensions of the plates to minimize non-uniform electric field due to the irregular distribution of charges near the edges.
Let Q = electric charge on the capacitor
∴σ = Q / A = surface charge density
As d is very small, the plates can be considered as infinitely charged planes and the electric field between the plates can therefore be considered uniform.The electric fields, E1 and E2, between the plates due to positively charged and negatively charged plates respectively are equal in magnitude and direction. The direction of both E1 and E2 is from the positively charged plate to the negatively charged plate. The resultant electric field between the plates is, therefore,
The end to end connection of capacitors as shown In the figure is called the series connection of capacitors. Equal charge Q deposits on each capacitor, but the p.d. between their plates is different depending on the value of its capacitance.
∴ V = V1 + V2 + …. + Vn
The connection of capacitors in which positive plates of all capacitors are connected to a single point and negative plates to another single point in a circuit is called parallel connection of capacitors as shown in the figure. In such a connection, charge accumulated on each of the capacitors is different depending on the value of its capacitance, but the p.d. across all is the same.
The negative charge induced on the second sphere reduces the electric potential of the first sphere thereby increasing its charge storage capacity. The ratio Q / V of the charge on the first sphere and the potential difference between the two spheres is still constant and is called the capacitance C of the system. The value of C depends on the dimensions of the spheres, the distance between the two spheres and the medium between them. The arrangement in which two good conductors of arbitrary shape and volume, are arranged close to one another, but separated from each other, is called a capacitor. The conductors are known as plates of the capacitor. Positively charged conductor is called the positive plate and the negatively charged conductor the negative plate. Both the plates are equally charged. The charge on the positive plate is called the charge ( Q ) of the capacitor and taking the potential difference between the two plates as V, capacitance of the capacitor is C = Q / V. The S.I. unit of capacitance is coulomb / volt which is also called farad ( F ) named after the great scientist Michael Faraday. The smaller units of farad are microfarad ( m F = 10 (exp- 6) F ) and picofarad ( pF = 10 (exp-12) F ).Parallel Plate Capacitor: -
This type of capacitor is made by two metallic plates having identical area and kept parallel to each other. The distance ( d ) between the two plates is kept less as compared to the dimensions of the plates to minimize non-uniform electric field due to the irregular distribution of charges near the edges.Let Q = electric charge on the capacitor
∴σ = Q / A = surface charge density
As d is very small, the plates can be considered as infinitely charged planes and the electric field between the plates can therefore be considered uniform.The electric fields, E1 and E2, between the plates due to positively charged and negatively charged plates respectively are equal in magnitude and direction. The direction of both E1 and E2 is from the positively charged plate to the negatively charged plate. The resultant electric field between the plates is, therefore,
E = E1 + E2 = σ + σ = σ / ε0 = Q / ε0A (because σ = Q / A)
2ε0 2ε0
Outside the plates, E1 and E2 being oppositely directed cancel each other resulting in zero electric field in this region. The potential difference between the two plates is
V = E d = Q d / ε0 A
because the capacitance of the capacitor, C = Q /V = ε0 A / d
( a ) Series Connection of Capacitors: -
The end to end connection of capacitors as shown In the figure is called the series connection of capacitors. Equal charge Q deposits on each capacitor, but the p.d. between their plates is different depending on the value of its capacitance.∴ V = V1 + V2 + …. + Vn
= Q / C1 + Q / C2 + Q / C 3 + --------- + Q / C n
dividing both sides by Q we get the following equation i.e.
V / Q = 1 / C1 + 1 . C 2 + 1 / C3 + ------- + 1 / Cn When all capacitors connected in series are replaced by a single capacitor of capacitance C such that the charge deposited on it is Q with the same voltage supply, then such a capacitor is called their equivalent capacitor.
Now as V / Q = 1 / C (because Q / V = C) so above equation becomes
1 / C = 1 / C1 + 1 / C2 + 1/ C3 + ------- + 1 / Cn
The value of C is smaller than the smallest of C1, C2, …. Cn.
( b ) Parallel Connection of Capacitors: -
The connection of capacitors in which positive plates of all capacitors are connected to a single point and negative plates to another single point in a circuit is called parallel connection of capacitors as shown in the figure. In such a connection, charge accumulated on each of the capacitors is different depending on the value of its capacitance, but the p.d. across all is the same.Thus, total charge Q = Q1 + Q2 + Q3 + ….
= ( C1 + C2 + C3 + …. ) V
When all capacitors connected in parallel are replaced by a single capacitor of capacitance C such that the charge deposited on it is Q with the same voltage supply, then such a capacitor is called their equivalent capacitor. Its value is
C = Q / V = C1 + C2 + C3 + ….
= ( C1 + C2 + C3 + …. ) V
When all capacitors connected in parallel are replaced by a single capacitor of capacitance C such that the charge deposited on it is Q with the same voltage supply, then such a capacitor is called their equivalent capacitor. Its value is
C = Q / V = C1 + C2 + C3 + ….
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