Important Formulas: Electrostatic Potential and Capacitance | Physics Class 12 - NEET PDF Download

 Page 1


CAPACITANCE
1. (i) q  ? V ? q =  CV
q : Charge on positive plate of the capacitor
C : Capacitance of capacitor.
V : Potential difference between positive and negative plates.
(ii) Representation of capacitor :   ,
  (
(iii) Energy stored in the capacitor : U =
2
1
CV
2
 = 
C 2
Q
2
= 
2
QV
(iv) Energy density =  
2
1
 ?
?
?
r 
E
2 
= 
2
1
?
?
?
K E
2
?
r 
= Relative permittivity of the medium.
K= 
  
?
r 
: Dielectric Constant
For vacuum, energy density =  
2
1
?
?
E
2
(v) Types of Capacitors :
(a) Parallel plate capacitor
C =
d
A
r 0
? ?
   =  K 
d
A
0
?
A : Area of plates
d : distance between the plates( << size of plate )
(b) Spherical Capacitor :
? Capacitance of an isolated spherical Conductor (hollow or solid )
C= 4 ? ? ?
?
?
r 
R
R = Radius of the spherical conductor
? Capacitance of spherical capacitor
C= 4 ? ?
?
) a b (
ab
?
            
1
2 b
a
? C = 
) a b (
ab K 4
2 0
?
? ?
K
1 K
2 K
3
b
a
Page 2


CAPACITANCE
1. (i) q  ? V ? q =  CV
q : Charge on positive plate of the capacitor
C : Capacitance of capacitor.
V : Potential difference between positive and negative plates.
(ii) Representation of capacitor :   ,
  (
(iii) Energy stored in the capacitor : U =
2
1
CV
2
 = 
C 2
Q
2
= 
2
QV
(iv) Energy density =  
2
1
 ?
?
?
r 
E
2 
= 
2
1
?
?
?
K E
2
?
r 
= Relative permittivity of the medium.
K= 
  
?
r 
: Dielectric Constant
For vacuum, energy density =  
2
1
?
?
E
2
(v) Types of Capacitors :
(a) Parallel plate capacitor
C =
d
A
r 0
? ?
   =  K 
d
A
0
?
A : Area of plates
d : distance between the plates( << size of plate )
(b) Spherical Capacitor :
? Capacitance of an isolated spherical Conductor (hollow or solid )
C= 4 ? ? ?
?
?
r 
R
R = Radius of the spherical conductor
? Capacitance of spherical capacitor
C= 4 ? ?
?
) a b (
ab
?
            
1
2 b
a
? C = 
) a b (
ab K 4
2 0
?
? ?
K
1 K
2 K
3
b
a
(c) Cylindrical Capacitor :   ? >> {a,b}
Capacitance per unit length = 
) a / b ( n
2
?
?
? ?
?
F/m    
b
?
(vi) Capacitance of capacitor depends on
(a) Area of plates
(b) Distance between the plates
(c) Dielectric medium between the plates.
(vii) Electric field intensity between the plates of capacitor
E =
0
?
?
 ? 
d
V
? ? ? ?Surface change density
(viii) Force experienced by any plate of capacitor : F =  
0
2
A 2
q
?
2. DISTRIBUTION OF CHARGES ON CONNECTING TWO  CHARGED
CAPACITORS:
When two capacitors are C
1 
 and C
2 
are 
 
connected as shown in figure
(a) Common potential :
? V = 
2 1
2 2 1 1
C C
V C V C
?
?
 = 
ce tan capaci Total
e arg ch Total
(b) Q
1
'
 
= C
1
V = 
2 1
1
C C
C
?
(Q
1
 + Q
2
)
Q
2
' = C
2
 V = 
2 1
2
C C
C
?
 (Q
1
 +Q
2
)
Page 3


CAPACITANCE
1. (i) q  ? V ? q =  CV
q : Charge on positive plate of the capacitor
C : Capacitance of capacitor.
V : Potential difference between positive and negative plates.
(ii) Representation of capacitor :   ,
  (
(iii) Energy stored in the capacitor : U =
2
1
CV
2
 = 
C 2
Q
2
= 
2
QV
(iv) Energy density =  
2
1
 ?
?
?
r 
E
2 
= 
2
1
?
?
?
K E
2
?
r 
= Relative permittivity of the medium.
K= 
  
?
r 
: Dielectric Constant
For vacuum, energy density =  
2
1
?
?
E
2
(v) Types of Capacitors :
(a) Parallel plate capacitor
C =
d
A
r 0
? ?
   =  K 
d
A
0
?
A : Area of plates
d : distance between the plates( << size of plate )
(b) Spherical Capacitor :
? Capacitance of an isolated spherical Conductor (hollow or solid )
C= 4 ? ? ?
?
?
r 
R
R = Radius of the spherical conductor
? Capacitance of spherical capacitor
C= 4 ? ?
?
) a b (
ab
?
            
1
2 b
a
? C = 
) a b (
ab K 4
2 0
?
? ?
K
1 K
2 K
3
b
a
(c) Cylindrical Capacitor :   ? >> {a,b}
Capacitance per unit length = 
) a / b ( n
2
?
?
? ?
?
F/m    
b
?
(vi) Capacitance of capacitor depends on
(a) Area of plates
(b) Distance between the plates
(c) Dielectric medium between the plates.
(vii) Electric field intensity between the plates of capacitor
E =
0
?
?
 ? 
d
V
? ? ? ?Surface change density
(viii) Force experienced by any plate of capacitor : F =  
0
2
A 2
q
?
2. DISTRIBUTION OF CHARGES ON CONNECTING TWO  CHARGED
CAPACITORS:
When two capacitors are C
1 
 and C
2 
are 
 
connected as shown in figure
(a) Common potential :
? V = 
2 1
2 2 1 1
C C
V C V C
?
?
 = 
ce tan capaci Total
e arg ch Total
(b) Q
1
'
 
= C
1
V = 
2 1
1
C C
C
?
(Q
1
 + Q
2
)
Q
2
' = C
2
 V = 
2 1
2
C C
C
?
 (Q
1
 +Q
2
)
(c) Heat loss during redistribution :
?H = U
i
 – U
f 
= 
2
1
 
2 1
2 1
C C
C C
?
 (V
1
 – V
2
)
2
The loss of energy is in the form of Joule heating in the wire.
3. Combination of capacitor :
(i) Series Combination
3 2 1 eq
C
1
C
1
C
1
C
1
? ? ?
3 2 1
3 2 1
C
1
:
C
1
:
C
1
V : V : V ?
+Q
V
1
V
2
V
3
C
2
C
1
C
3
–Q +Q –Q +Q –Q
(ii) Parallel Combination :
Q+ –Q
C
3
C
2
C
1
V
Q+ –Q
Q+ –Q
C
eq 
= C
1
 + C
2
 + C
3
Q
1
: Q
2
 :Q
3 
= C
1 
: C
2 
: C
3
4. Charging and Discharging of  a  capacitor :
(i) Charging of Capacitor ( Capacitor initially uncharged ):
q = q
0 
( 1 – e
– t / ?
)
R
V C
q
0 
= Charge on the capacitor at steady state
q
0
 = CV
Page 4


CAPACITANCE
1. (i) q  ? V ? q =  CV
q : Charge on positive plate of the capacitor
C : Capacitance of capacitor.
V : Potential difference between positive and negative plates.
(ii) Representation of capacitor :   ,
  (
(iii) Energy stored in the capacitor : U =
2
1
CV
2
 = 
C 2
Q
2
= 
2
QV
(iv) Energy density =  
2
1
 ?
?
?
r 
E
2 
= 
2
1
?
?
?
K E
2
?
r 
= Relative permittivity of the medium.
K= 
  
?
r 
: Dielectric Constant
For vacuum, energy density =  
2
1
?
?
E
2
(v) Types of Capacitors :
(a) Parallel plate capacitor
C =
d
A
r 0
? ?
   =  K 
d
A
0
?
A : Area of plates
d : distance between the plates( << size of plate )
(b) Spherical Capacitor :
? Capacitance of an isolated spherical Conductor (hollow or solid )
C= 4 ? ? ?
?
?
r 
R
R = Radius of the spherical conductor
? Capacitance of spherical capacitor
C= 4 ? ?
?
) a b (
ab
?
            
1
2 b
a
? C = 
) a b (
ab K 4
2 0
?
? ?
K
1 K
2 K
3
b
a
(c) Cylindrical Capacitor :   ? >> {a,b}
Capacitance per unit length = 
) a / b ( n
2
?
?
? ?
?
F/m    
b
?
(vi) Capacitance of capacitor depends on
(a) Area of plates
(b) Distance between the plates
(c) Dielectric medium between the plates.
(vii) Electric field intensity between the plates of capacitor
E =
0
?
?
 ? 
d
V
? ? ? ?Surface change density
(viii) Force experienced by any plate of capacitor : F =  
0
2
A 2
q
?
2. DISTRIBUTION OF CHARGES ON CONNECTING TWO  CHARGED
CAPACITORS:
When two capacitors are C
1 
 and C
2 
are 
 
connected as shown in figure
(a) Common potential :
? V = 
2 1
2 2 1 1
C C
V C V C
?
?
 = 
ce tan capaci Total
e arg ch Total
(b) Q
1
'
 
= C
1
V = 
2 1
1
C C
C
?
(Q
1
 + Q
2
)
Q
2
' = C
2
 V = 
2 1
2
C C
C
?
 (Q
1
 +Q
2
)
(c) Heat loss during redistribution :
?H = U
i
 – U
f 
= 
2
1
 
2 1
2 1
C C
C C
?
 (V
1
 – V
2
)
2
The loss of energy is in the form of Joule heating in the wire.
3. Combination of capacitor :
(i) Series Combination
3 2 1 eq
C
1
C
1
C
1
C
1
? ? ?
3 2 1
3 2 1
C
1
:
C
1
:
C
1
V : V : V ?
+Q
V
1
V
2
V
3
C
2
C
1
C
3
–Q +Q –Q +Q –Q
(ii) Parallel Combination :
Q+ –Q
C
3
C
2
C
1
V
Q+ –Q
Q+ –Q
C
eq 
= C
1
 + C
2
 + C
3
Q
1
: Q
2
 :Q
3 
= C
1 
: C
2 
: C
3
4. Charging and Discharging of  a  capacitor :
(i) Charging of Capacitor ( Capacitor initially uncharged ):
q = q
0 
( 1 – e
– t / ?
)
R
V C
q
0 
= Charge on the capacitor at steady state
q
0
 = CV
? ? ? ?Time constant  = CR
eq.
I = 
?
0
q
 e 
– t / ? ?
? ? ?
R
V
e
– t / ?
(ii) Discharging of Capacitor :
q = q
0
 e 
– t / ?
q
0
 = Initial charge on the capacitor
I = 
?
0
q
 e 
– t / ?
R
C
     
q
0
0.37v
0
?
t
q
 5. Capacitor with dielectric :
(i) Capacitance in the presence of dielectric :
C = 
d
A K
0
?
 = KC
0
+ + + + + + + + + + + + + +
? ? ?
0
+ + ?
– – ?
V
?
b
+
– ?
b – – – – – – – – – – –
? ? ?
0 b
C
0
 = Capacitance in the absence of dielectric.
Page 5


CAPACITANCE
1. (i) q  ? V ? q =  CV
q : Charge on positive plate of the capacitor
C : Capacitance of capacitor.
V : Potential difference between positive and negative plates.
(ii) Representation of capacitor :   ,
  (
(iii) Energy stored in the capacitor : U =
2
1
CV
2
 = 
C 2
Q
2
= 
2
QV
(iv) Energy density =  
2
1
 ?
?
?
r 
E
2 
= 
2
1
?
?
?
K E
2
?
r 
= Relative permittivity of the medium.
K= 
  
?
r 
: Dielectric Constant
For vacuum, energy density =  
2
1
?
?
E
2
(v) Types of Capacitors :
(a) Parallel plate capacitor
C =
d
A
r 0
? ?
   =  K 
d
A
0
?
A : Area of plates
d : distance between the plates( << size of plate )
(b) Spherical Capacitor :
? Capacitance of an isolated spherical Conductor (hollow or solid )
C= 4 ? ? ?
?
?
r 
R
R = Radius of the spherical conductor
? Capacitance of spherical capacitor
C= 4 ? ?
?
) a b (
ab
?
            
1
2 b
a
? C = 
) a b (
ab K 4
2 0
?
? ?
K
1 K
2 K
3
b
a
(c) Cylindrical Capacitor :   ? >> {a,b}
Capacitance per unit length = 
) a / b ( n
2
?
?
? ?
?
F/m    
b
?
(vi) Capacitance of capacitor depends on
(a) Area of plates
(b) Distance between the plates
(c) Dielectric medium between the plates.
(vii) Electric field intensity between the plates of capacitor
E =
0
?
?
 ? 
d
V
? ? ? ?Surface change density
(viii) Force experienced by any plate of capacitor : F =  
0
2
A 2
q
?
2. DISTRIBUTION OF CHARGES ON CONNECTING TWO  CHARGED
CAPACITORS:
When two capacitors are C
1 
 and C
2 
are 
 
connected as shown in figure
(a) Common potential :
? V = 
2 1
2 2 1 1
C C
V C V C
?
?
 = 
ce tan capaci Total
e arg ch Total
(b) Q
1
'
 
= C
1
V = 
2 1
1
C C
C
?
(Q
1
 + Q
2
)
Q
2
' = C
2
 V = 
2 1
2
C C
C
?
 (Q
1
 +Q
2
)
(c) Heat loss during redistribution :
?H = U
i
 – U
f 
= 
2
1
 
2 1
2 1
C C
C C
?
 (V
1
 – V
2
)
2
The loss of energy is in the form of Joule heating in the wire.
3. Combination of capacitor :
(i) Series Combination
3 2 1 eq
C
1
C
1
C
1
C
1
? ? ?
3 2 1
3 2 1
C
1
:
C
1
:
C
1
V : V : V ?
+Q
V
1
V
2
V
3
C
2
C
1
C
3
–Q +Q –Q +Q –Q
(ii) Parallel Combination :
Q+ –Q
C
3
C
2
C
1
V
Q+ –Q
Q+ –Q
C
eq 
= C
1
 + C
2
 + C
3
Q
1
: Q
2
 :Q
3 
= C
1 
: C
2 
: C
3
4. Charging and Discharging of  a  capacitor :
(i) Charging of Capacitor ( Capacitor initially uncharged ):
q = q
0 
( 1 – e
– t / ?
)
R
V C
q
0 
= Charge on the capacitor at steady state
q
0
 = CV
? ? ? ?Time constant  = CR
eq.
I = 
?
0
q
 e 
– t / ? ?
? ? ?
R
V
e
– t / ?
(ii) Discharging of Capacitor :
q = q
0
 e 
– t / ?
q
0
 = Initial charge on the capacitor
I = 
?
0
q
 e 
– t / ?
R
C
     
q
0
0.37v
0
?
t
q
 5. Capacitor with dielectric :
(i) Capacitance in the presence of dielectric :
C = 
d
A K
0
?
 = KC
0
+ + + + + + + + + + + + + +
? ? ?
0
+ + ?
– – ?
V
?
b
+
– ?
b – – – – – – – – – – –
? ? ?
0 b
C
0
 = Capacitance in the absence of dielectric.
(ii) E
in
 = E – E
ind
 = 
0
?
?
 – 
0
b
?
?
 = 
0
K ?
?
 = 
d
V
E : 
0
?
?
  Electric field in the absence of dielectric
E
ind
 : Induced (bound) charge density.
(iii) ?
b
 = ?(1 – 
K
1
).
6. Force on dielectric
(i) When battery is connected
d 2
V ) 1 K ( b
F
2
0
? ?
?
+
–
b
b
?
?
d
? ? ?
F
x
(ii) When battery is not connected F = 
2
2
C 2
Q
 
dx
dC
* Force on the dielectric will be zero when the dielectric is fully inside.