# Chapter 5 Capacitor¶

## Example 5.1 Page no 108¶

In [5]:
#Given
r=6.4*10**6          #m
t=9*10**9

#Calculation
C=r/t

#Result
print"The capacitance is",round(C*10**6,0),"F"

The capacitance is 711.0 F


## Example 5.2 Page no 108¶

In [25]:
#Given
r=0.01              #m
q=1                 #C
d=9.0*10**9

#Calculation
V=(q*d)/r

#Result
print"V=",V,"V"
print"The given metal sphere will not be able to hold charge of 1 C"

V= 9e+11 V
The given metal sphere will not be able to hold charge of 1 C


## Example 5.3 Page no 109¶

In [28]:
#Given
R=3
Q=27
q=4*220

#Calculation
d=(Q*q)/(4*R)

#Result
print"The potential of the bigger drop is",d,"V"

The potential of the bigger drop is 1980 V


## Example 5.4 Page no 109¶

In [36]:
#Given
C=2               #F
d=0.5*10**-2      #m
a=8.854*10**-12

#Calculation
Q=(C*d)/a

#Result
print"Area of the plate is", round(Q*10**-9,2),"*10**9 m**2"

Area of the plate is 1.13 *10**9 m**2


## Example 5.5 Page no 109¶

In [40]:
#Given
A=10**-2                         #m**2
d=10**-3                           #m
q=0.12*10**-6
V=120.0
e=8.85*10**-12

#Calculation
C=q/V
K=C*d/(e*A)

#Result
print"Dielectric constant of the material is", round(K,1)

Dielectric constant of the material is 11.3


## Example 5.6 Page no 109¶

In [43]:
#Given
A1=100.0                            #cm**2
A2=500                             #cm**2
d1=0.05                            #cm

#Calculation
d2=(A2*d1)/A1

#Result
print"Difference between the plates of second capacitor is", d2,"cm"

Difference between the plates of second capacitor is 0.25 cm


## Example 5.7 Page no 109¶

In [48]:
#Given
a=6.45*10**6                      #m
b=6.4*10**6                       #m
m=9*10**9

#Calculation
C=(a*b)/(m*(a-b))

#Result
print"Capacitance of the spherical capacitor is",round(C,3),"F"

Capacitance of the spherical capacitor is 0.092 F


## Example 5.8 Page no 109¶

In [61]:
#Given
a=12*10**-2                     #m
b=13*10**-2                      #m
q=2.5*10**-6                    #C
K=32
m=9.0*10**9

#Calculation
C=(K*a*b)/(m*(b-a))
V=q/C
C1=a/m
C2=C/C1

#Result
print"(a) Capacitance of the capacitor is", round(C*10**9,3)*10**-9,"F"
print"(b) Potential of the inner sphere is", round(V,1),"V"
print"(c) Capacitance of the capacitor is",C2

(a) Capacitance of the capacitor is 5.547e-09 F
(b) Potential of the inner sphere is 450.7 V
(c) Capacitance of the capacitor is 416.0


## Example 5.9 Page no 110¶

In [10]:
#Given
a=1.4*10**-2                       #m
b=1.5*10**-2                        #m
q=3.5*10**-6                        #C
e=8.854*10**-12
l=15*10**-2

#Calculation
import math
C=(2*math.pi*e*l)/(2.303*math.log10(b/a))
V=q/C

#Result
print"Capacitance of the system is", round(C*10**10,2)*10**-8,"F"
print"Potential of the inner cylinder is", round(V*10**-4,2),"*10**4 V"

Capacitance of the system is 1.21e-08 F
Potential of the inner cylinder is 2.89 *10**4 V


## Example 5.10 Page no 110¶

In [17]:
#Given
C=9.0*10**-12                     #F
V=120                           #V

#Calculation
C1=1/(3/C)
q=(V*C)/3.0
V1=q/C

#Result
print"(a) Total capacitance is",C1,"F"
print"(b) Potential difference across each capacitor is",V1,"V"

(a) Total capacitance is 3e-12 F
(b) Potential difference across each capacitor is 40.0 V


## Example 5.11 Page no 110¶

In [26]:
#Given
C1=2*10**-12                           #F
C2=3*10**-12
C3=4*10**-12
V=100                                  #Volts

#Calculation
C=C1+C2+C3
q1=C1*V
q2=C2*V
q3=C3*V

#Result
print"(a) Total capacitamce of the parallel combination is",C,"F"
print"(b) Charge on q1 is",q1,"C"
print"(c) Charge on q2 is",q2,"C"
print"(d) Charge on q3 is",q3,"C"

(a) Total capacitamce of the parallel combination is 9e-12 F
(b) Charge on q1 is 2e-10 C
(c) Charge on q2 is 3e-10 C
(d) Charge on q3 is 4e-10 C


## Example 5.12 Page no 110¶

In [31]:
#Given
c1=5.0                  #micro F
c2=4.0
c3=3.0

#Calculation
C=1/(1/c1+1/c2)
c11=C+c3

#Result
print"Capacitance of the combination is",round(c11,2),"micro F"

Capacitance of the combination is 5.22 micro F


## Example 5.13 Page no 111¶

In [35]:
#Given
cs=3                     #micro F
cp=16
c1=12

#Calculation
C=cs*cp
c2=cp-c1

#Result
print"Capacitance of each capacitor is",c2,"micro F"

Capacitance of each capacitor is 4 micro F


## Example 5.14 Page no 111¶

In [39]:
#Given
c2=6.0                #micro F
c3=6.0
c1=12.0
c4=12.0

#Calculation
c23=c2+c3
C=1/(1/c1+1/c23+1/c4)

#Result
print"resultant of capacitance is",C,"micro F"

resultant of capacitance is 4.0 micro F


## Example 5.15 Page no 111¶

In [43]:
#Given
c1=3.0                     #pico F
c2=2.0

#Calculation
C=1/(1/c1+1/c2+1/c1)
c11=C+c2
C11=1/(1/c1+1/c11+1/c1)

#Result
print"Resultant capacitance is",round(C11,0),"pF"

Resultant capacitance is 1.0 pF


## Example 5.16 Page no 111¶

In [49]:
#Given
C2=2
C3=2
C1=1                   #micro F
C4=2
C5=1

#Calculation
C23=C2*C3/(C2+C3)
C123=C1+C23
C1234=C123*C4/(C123+C4)
C=C1234+C5

#Ressult
print"Equivalent capacitance is", C,"micro F"

Equivalent capacitance is 2 micro F


## Example 5.17 Page no 112¶

In [75]:
#Given
C5=10*10**-6                            #micro F
C6=10*10**-6
C2=60.0*10**-6
C3=60.0*10**-6
C4=60.0*10**-6
C1=40*10**-6
V=100                              #V

#Calculation
C56=(C5+C6)
C234=1/(1/C2+1/C3+1/C4)
C=C56+C234
C11=(C1*C)/(C1+C)
q=C56*V

#Result
print"Total charge is",q*10**3,"*10**-3 C"
print"Equivalent capacitance is",C11*10**6,"micro F"

Total charge is 2.0 *10**-3 C
Equivalent capacitance is 20.0 micro F


## Example 5.19 Page no 113¶

In [81]:
#Given
C1=5.0*10**-6                            #F
C2=10.0*10**-6
C3=2.0*10**-6
C4=4.0*10**-6

#Calculation
C12=1/(1/C1+1/C2)
C34=1/(1/C3+1/C4)
C=C12+C34

#Result
print"Effective capacitance is", round(C*10**6,2),"micro F"

Effective capacitance is 4.67 micro F


## Example 5.20 Page no 113¶

In [84]:
#Given
n=3
C1=1.0
C2=1.0
C3=1.0
C=2                           #micro F

#Calculation
C11=1/(1/C1+1/C2+1/C3)
m=C/C11

#Result
print"Capacitance required is", m

Capacitance required is 6.0


## Example 5.21 Page no 113¶

In [88]:
#Given
C1=4
V=6
C2=6

#Calculation
q1=C1*V
q2=C2*V

#Result
print"Charge on C1 is",q1,"micro C"
print"Charge on C2 is",q2,"micro C"

Charge on C1 is 24 micro C
Charge on C2 is 36 micro C


## Example 5.22 Page no 114¶

In [94]:
#Given
C2=5                   #micro F
C3=5
a=6
C1=10
V=3

#Calculation
C23=C2+C3
V1=a/2.0
q1=C1*V
q23=C23*V
q3=q23/2.0

#Result
print"Charge on capacitor C1 is",q1,"micro F"
print"Charge on capacitor C2 is",q23,"micro F"
print"Charge on capacitor C3 is",q3,"micro F"

Charge on capacitor C1 is 30 micro F
Charge on capacitor C2 is 30 micro F
Charge on capacitor C3 is 15.0 micro F


## Example 5.23 Page no 114¶

In [101]:
#Given
C1=4*10**-6                   #F
V1=400                        #V
C2=2*10**-6
q2=0

#Calculation
q1=C1*V1
C=C1+C2
q=q1+q2
V=q/C

#Result
print"Common potential is", round(V,2),"V"

Common potential is 266.67 V


## Example 5.24 Page no 114¶

In [105]:
#Given
V=12
C1=8                         #micro F
C2=4

#Calculation
Va=V-C2
Vb=V-C1
V1=Va-Vb

#Result
print"Potential difference is", V1,"V"

Potential difference is 4 V


## Example 5.25 Page no 114¶

In [112]:
#Given
A=90*10**-4                                 #m**2
d=2.5*10**-3                                #m
V=400                                       #Volts
e=8.854*10**-12

#Calculation
C=(e*A)/d
W=(C*V**2)/2.0

#Result
print"Electrostatic energy is", round(W*10**6,2)*10**-6,"J"

Electrostatic energy is 2.55e-06 J


## Example 5.26 Page no 114¶

In [119]:
#Given
C=2000*10**-6
V=1.5                   #V
t=10.0**-4                #s

#Calculation
U=(C*V**2)/2.0
P=U/t

#Result
print"Energy stored in the capacitor is", U*10**3,"*10**-3 J"
print"Power of the flash is",P,"W"

Energy stored in the capacitor is 2.25 *10**-3 J
Power of the flash is 22.5 W


## Example 5.27 Page no 115¶

In [129]:
#Given
C1=4*10**-6
V1=200                              #V
C2=2*10**-6                                # F

#Calculation
U1=(C1*V1**2)/2.0
q=C1*V1
C=C1+C2
V=q/C
U2=(C*V**2)/2.0
U=U1-U2

#Result
print"Electrostatic energy is",round(U*10**2,2),"*10**-2 J"

Electrostatic energy is 2.67 *10**-2 J


## Example 5.28 Page no 115¶

In [135]:
#Given
K=6.0
C=17.7*10**-12                    #F
V=100

#Calculation
C1=K*C
q=C1*V
V1=V/K
q1=C1*V1

#Result
print"(a) Charge on capacitor is", q,"C"
print"(b) Charge on capacitor is", q1,"C"

(a) Charge on capacitor is 1.062e-08 C
(b) Charge on capacitor is 1.77e-09 C


## Example 5.29 Page no 115¶

In [140]:
#Given
K=3
e=8.854*10**-12                         #C**2/N/m**2
C=50*10**-12                              #F
a=10**7                                  #V/m
b=10
V=10**3

#Calculation
E=(a*b)/100.0
q=C*V
A=q/(e*K*E)

#Result
print"Minimum area is", round(A*10**4,1),"cm**2"

Minimum area is 18.8 cm**2


## Example 5.30 Page no 115¶

In [144]:
#Given
V=15*10**5                        #V
E=5.0*10**7                         #V/m

#Calculation
r=V/E

#Result
print"Minimum radius of the spherical shell is", r*10**2,"cm"

Minimum radius of the spherical shell is 3.0 cm