This document discusses capacitance and capacitors. It defines a capacitor as an electrical device that can store charge. A capacitor consists of two conducting plates separated by an insulating material. It explains that capacitance is the ability of a conductor to store charge, and is proportional to the area of the plates and inversely proportional to the distance between them. It also discusses how capacitors can be grouped in series or parallel configurations and the equations to calculate their equivalent capacitance. Finally, it covers the energy stored in a capacitor and how that energy is lost when charges are shared between capacitors.

2. CAPACITANCE
BY DIBYA PRASAD SAHOO

3. CAPACITOR/CONDENSOR
• IT IS A CHARGE STORING ELECTRICAL DEVICE
• IT ESSENTIALLY CONSISTS OF 2 CONDUCTING SURFACES(METAL PLATES)
SEPARATED BY AN INSULATING MATERIAL(EX-AIR,MICA,PAPER ETC.
• IT HAS A PROPERTY TO STORE THE ENERGY AS POTENTIAL ENERGY IN
IT’S ELECTRIC FIELD
• IT PLAYS A VITAL ROLE IN AC AND DC CIRCUIT
• CAPACITORS ARE USED IN MANY ELECTRICAL CIRCUITS LIKE RADIO
TUNNING, IGNITION CIRCUIT OF ENGINE, IN FILTER CIRCUIT, IN FAN AND
MOTOR ETC.

4. CAPACITANCE
•THE CHARGE HOLDING ABILITY OF A CONDUCTOR IS CALLED IT’S CAPACITANCE OR CAPACITY.
QUALITATIVE DEFINATION
•THE CAPACITANCE OF A CONDUCTOR IS DEFINED AS THE RATIO OF THE CHARGE GIVEN TO THE CONDUCTOR TO THE POTENTIAL
RAISED DUE TO IT
•CAPACITANCE OF A CONDUCTOR DOESN’T DEPEND UPON CHARGE GIVEN TO IT,POTENTIAL RAISED DUE TO IT AND THE MATERIAL
BY WHICH THE CONDUCTOR OR PLATES ARE MADE UP OF. HOWEVER IT DEPENDS UPON THE GEOMETRY (i.e. SHAPE & SIZE) AND
THE INTERVENING MEDIUM (i.e. DIELECTRIC)
QUANTITATIVE DEFINATION
•SI UNIT OF CAPACITANCE IS FARAD(F)
•C.G.S UNIT OF CAPACITANCE IS STAT. F
•1F=1COULOMB/1VOLT=9×1011STAT-F
•DIMENSION=Q/V=𝐴2 𝑇2/𝑀1 𝐿2 𝑇−2 = 𝑀−1 𝐿−2 𝑇4 𝐴2
UNIT AND DIMENSION

5. PRINCIPLE OF CAPACITOR
 WHENEVER AN EARTHED CONDUCTOR IS PLACED NEAR A CHARGED
CONDUCTOR THE CAPACITANCE OF THE SYSTEM INCREASES
CONSIDERABLY.
+ + -
+ + -
+ + -
+ + -
+ + -
 EXPLANATION
THE INDUCED NEGATIVE CHARGE ON THE INNER SURFACE OF EARTHED
CONDUCTOR REDUCES THE POTENTIAL ON THE CHARGED CONDUCTOR.
HENCE A SURPLUS AMOUNT OF CHARGE CAN BE ADDED TO THE CHARGED
CONDUCTOR i.e. CAPACITANCE OF THE SYSTEM INCREASES
+q -q

6. CAPACITANCEOF A PARALLEL PLATEAIR CAPACITOR
 LET US CONSIDER A PARALLEL PLATE AIR CAPACITOR CONSISTING OF TWO PARALLEL PLATE M AND N
SEPARATED BY A DISTANCE (D) HAVING AIR IN BETWEEN THEM.LET THE PLATE(M) IS CHARGED BY AN
AMOUNT(+q)WHILE THE OUTER SURFACE OF PLATE(N) IS EARTHED.AS A RESULT OF INDUCTION AN
EQUAL OF INDUCTION AN EQUAL AMOUNT OF NEGATIVE CHARGE(-q) IS INDUCED AT THE INNER
SURFACE OF THE PLATE(N).
+ + -
+ + -
+ + -
+ + -
+ + _
d
EXPRESSION FOR CAPACITANCE
 𝐸 = 𝜎/2𝜀0+𝜎/2𝜀0=𝜎/𝜀0=𝑞/𝐴𝜀0 where 𝜎 = 𝑆𝑈𝑅𝐹𝐴𝐶𝐸 𝐶𝐻𝐴𝑅𝐺𝐸 𝐷𝐸𝑁𝑆𝐼𝑇𝑌
𝐸=𝑣/𝑑 ⇒
𝑞
𝐴𝜀0
=
𝑣
𝑑
⇒
𝑞
𝑣
=
𝜀0 𝐴
𝑑
⇒ 𝐶0 =
𝜀0 𝐴
𝑑
 HENCE CAPACITANCE OF A PARALLEL CAPACITOR IS DIRECTLY PROPORTIONAL TO THE AREA OF
THE PLATES AND INVERSELY PROPORTIONAL TO THE SEPARATION BETWEEN THE PLATES.
+q -q

7. CAPACITANCE OF A PARALLEL PLATE AIR CAPACITOR WITH PARTIALLY
FILLED DIELECTRIC
 LET US CONSIDER A PARALLEL PLATE AIR CAPACITOR CONSISTING OF TWO PARALLEL PLATE
CAPACITOR HAVING SEPARATION(d) WITH A DIELECTRIC SLAB OF THICKNESS(t) BETWEEN
THEM.LET k BE THE DIELECTRIC CONSTANT OF THE MATERIAL OF THE SLAB AND A BE THE AREA OF
EITHER PLATE.
+ + -
+ + -
+ + -
+ + -
+ + -
t
d
EXPRESSION FOR CAPACITANCE
 𝐸0 =
𝜎
𝜀0
& 𝐸 =
𝜎
𝜀
=
𝜎
𝑘𝜀0
where 𝜎 = 𝑆𝑈𝑅𝐹𝐴𝐶𝐸 𝐶𝐻𝐴𝑅𝐺𝐸 𝐷𝐸𝑁𝑆𝐼𝑇𝑌
𝑣 = 𝐸0 𝑑 − 𝑡 + 𝐸𝑡 =
𝜎
𝜀0
𝑑 − 𝑡 +
𝑡
𝑘
=
𝑞
𝐴𝜀0
𝑑 − 𝑡 +
𝑡
𝑘
⇒
𝑞
𝑣
=
𝜀0 𝐴
𝑑−𝑡+
𝑡
𝑘
⇒ 𝑐 =
𝜀0 𝐴
𝑑−𝑡+
𝑡
𝑘
+q -q

8. GROUPING OF CAPACITOR
SERIES GROUPING
 THE CAPACITORS ARE SAID TO BE CONNECTED IN SERIES IF CHARGE ON EACH CAPACITOR IS
SAME.
1
𝐶 𝑆
=
1
𝐶1
+
1
𝐶2
+ ⋯ +
1
𝐶 𝑛
 CASE-1
FOR 2 CAPACITOR IN SERIES
1
𝐶 𝑆
=
1
𝐶1
+
1
𝐶2
⇒ 𝐶𝑆 =
𝐶1 𝐶2
𝐶1+𝐶2
 CASE-2
FOR 3 CAPACITOR IN SERIES
1
𝐶 𝑆
=
1
𝐶1
+
1
𝐶2
+
1
𝐶3
⇒ 𝐶𝑆 =
𝐶1 𝐶2 𝐶3
𝐶1 𝐶2+𝐶2 𝐶3+𝐶1 𝐶3
 CASE-3
FOR ‘n’ IDENTICAL CAPACITORS IN SERIES
1
𝐶 𝑆
=
𝑛
𝐶
⇒ 𝐶𝑆 =
𝐶
𝑛
PARALLEL GROUPING
 THE CAPACITORS ARE SAID TO BE CONNECTED IN SERIES IF POTENTIAL DIFFERENCE ACROSS EACH
CAPACITORS IS SAME.
𝐶𝑆 = 𝐶1 + 𝐶2 + 𝐶3 + ⋯ + 𝐶 𝑛

9. ELECTROSTATIC POTENTIAL ENERGY STORED IN A CAPACITOR
 IT IS THE AMOUNT OF WORKDONE TO CHARGE THE CAPACITOR.
AS 𝑑𝑤 = 𝑑𝑞 𝑣 ⇒ 𝑑𝑤 =
𝑞
𝑐
𝑑𝑞
 THEREFORE TOTAL WORKDONE BY THE BATTERY TO CHARGE THE
CAPACITOR TO IT’S MAXIMUM VALUE(𝑄)
𝑊 = 𝑑𝑊 =
1
𝐶 0
𝑄
𝑑𝑞
⇒ 𝑊 =
1
𝐶
𝑞2
2 0
𝑄
⇒ 𝑊 =
1
𝐶
𝑄2
2
− 0
⇒ 𝑊 =
𝑄2
2𝐶
 THE WORK IS BEING STORED AS POTENTIAL ENERGY IN THE CAPACITOR.
P.E(U)=
𝑄2
2𝐶
=
1
2
𝐶𝑉2=
1
2
𝑄𝑉

10. ENERGY DENSITY OF A CAPACITOR(𝑈𝑒)
 THE POTENTIAL ENERGY STORED PER UNIT VOLUME OF A CAPACITOR IS
CALLED THE ENERGY DENSITY OF THE CAPACITOR
𝑈𝑒 =
𝑃. 𝐸
𝑉𝑂𝐿𝑈𝑀𝐸
=
1
2
𝐶𝑉2
𝐴𝑑
=
𝑉2
2𝐴𝑑
𝜀0𝐴
𝑑
⇒ 𝑈𝑒 =
1
2
𝜀0
𝑉
𝑑
2
⇒ 𝑈𝑒 =
1
2
𝜀0 𝐸0
2
∵ 𝐸0 = −
𝑉
𝑑

11. SHARING OF CHARGES
 THE PHENOMENON BY WHICH THE CHARGE FLOWS FROM HIGHER
POTENTIAL TO ANOTHER BODY AT LOWER POTENTIAL IF THEY ARE
CONNECTED BY THE CONDUCTOR IS CALLED SHARING OF CHAGE.
 THE FLOW OF CHARGE CONTINUES TILL THE COMBINATION ACQUIRE A
COMMON POTENTIAL.
 IF 2 BODIES OF CAPACITANCE 𝐶1 AND 𝐶2 CHARGED TO THE POTENTIAL
𝑉1 AND 𝑉2 THEN TOTAL CHARGE BEFORE CONNECTION
⇒ 𝑞 = 𝑞1 + 𝑞2 = 𝐶1 𝑉1 + 𝐶2 𝑉2
 AFTER CONNECTION 𝑉 =
𝑇𝑂𝑇𝐴𝐿 𝐶𝐻𝐴𝑅𝐺𝐸
𝑇𝑂𝑇𝐴𝐿 𝐶𝐴𝑃𝐴𝐶𝐼𝑇𝐴𝑁𝐶𝐸
𝑉 =
𝐶1 𝑉1+𝐶2 𝑉2
𝐶1+𝐶2

12. LOSS OF ENERGY IN SHARING
𝞓𝑈 =
1
2
𝐶1 𝑉1
2
+
1
2
𝐶2 𝑉2
2
−
1
2
𝐶1 + 𝐶2 𝑉2
⇒ 𝞓𝑈 =
𝐶1 𝐶2
2 𝐶1+𝐶2
𝑉1
2
+ 𝑉2
2
− 2𝑉1 𝑉2
⇒ 𝞓𝑈 =
𝐶1 𝐶2
2 𝐶1+𝐶2
𝑉1 − 𝑉2
2

13. THANK YOU

14. THE END