Chapter 6: Capacitors and capacitance

Example 1, page no. 58

In [1]:
from __future__ import division
import math
#initializing  the  variables:
C1  =  4E-6;#  in  Farad
C2  =  50E-12;#  in  Farad
Q1  =  5E-3;#  in  Coulomb
V2  =  2000;#  in  volts

#calculation:
V1  =  Q1/C1
Q2  =  C2*V2

#Results
print  "\n\nResult\n\n"
print  "\n  (a)P.d  ",V1,"  Volts(V)\n"
print  "\n  (b)Charge(Q)  ",(Q2/1E-6),"  micro-Coulomb\n"


Result



  (a)P.d   1250.0   Volts(V)


  (b)Charge(Q)   0.1   micro-Coulomb

Example 2, page no. 58

In [2]:
from __future__ import division
import math
#initializing  the  variables:
I  =  4;#  in  amperes
C  =  20E-6;#  in  Farad
t  =  3E-3;#  in  sec

#calculation:
Q  =  I*t
V  =  Q/C

#Results
print  "\n\nResult\n\n"
print  "\n  (a)P.d  ",V,"  Volts(V)\n"


Result



  (a)P.d   600.0   Volts(V)

Example 3, page no. 59

In [3]:
from __future__ import division
import math
#initializing  the  variables:
I  =  2E-3;#  in  amperes
C  =  5E-6;#  in  Farad
V  =  800;#  in  volts

#calculation:
Q  =  C*V
t  =  Q/I

#Results
print  "\n\nResult\n\n"
print  "\n  capacitor  can  provide  an  average  discharge  current  for  ",t,"  Sec\n"


Result



  capacitor  can  provide  an  average  discharge  current  for   2.0   Sec

Example 4, page no. 60

In [5]:
from __future__ import division
import math
#initializing  the  variables:
Q  =  0.2E-6;#  in  Coulomb
A  =  800E-4;#  in  m2
d  =  0.005;#  in  m
V  =  250;#  in  Volts

#calculation:
D  =  Q/A
E  =  V/d

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Electric  flux  density  D  ",(D/1E-6)," uC/m2\n"
print  "\n  (b)Electric  field  strength  E  ",(E/1000),"  kV/m\n"


Result



  (a)Electric  flux  density  D   2.5  uC/m2


  (b)Electric  field  strength  E   50.0   kV/m

Example 5, page no. 60

In [6]:
from __future__ import division
import math
#initializing  the  variables:
D  =  2E-6;#  in  micro-C/m2
e0  =  8.85E-12;#  in  F/m
er  =  5;

#calculation:
E  =  D/(e0*er)

#Results
print  "\n\nResult\n\n"
print  "\n  Electric  field  strength  E  ",round((E/1000),2),"  kV/m\n"


Result



  Electric  field  strength  E   45.2   kV/m

Example 6, page no. 60

In [8]:
from __future__ import division
import math
#initializing  the  variables:
d  =  0.8E-3;#  in  m
e0  =  8.85E-12;#  in  F/m
era  =  1;#  for  air
erp  =  2.3;#  for  polythene
V  =200;#  in  Volts

#calculation:
E  =  V/d
#for  air
Da  =  E*e0*era
#for  polythene
Dp  =  E*e0*erp

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Electric  flux  density  for  air    ",round((Da/1E-6),2),"  micro-C/m2\n"
print  "\n  (b)Electric  flux  density  for  polythene    ",round((Dp/1E-6),2),"  micro-C/m2\n"


Result



  (a)Electric  flux  density  for  air     2.21   micro-C/m2


  (b)Electric  flux  density  for  polythene     5.09   micro-C/m2

Example 7, page no. 62

In [9]:
from __future__ import division
import math
#initializing  the  variables:
A  =  4E-4;#  in  m2
d  =  0.1E-3;#  in  m
e0  =  8.85E-12;#  in  F/m
er  =  100;
Q  =  1.2E-6;#  in  coulomb

#calculation:
C  =  e0*er*A/d
V  =  Q/C

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Capacitance    ",(C/1E-12),"  pF\n"
print  "\n  (b)P.d.=  ",round(V,2),"  Volts(V)\n"


Result



  (a)Capacitance     3540.0   pF


  (b)P.d.=   338.98   Volts(V)

Example 8, page no. 62

In [10]:
from __future__ import division
import math
#initializing  the  variables:
A  =  800E-4;#  in  m2
C  =  4425E-12;#  in  Farads
e0  =  8.85E-12;#  in  F/m
er  =  2.5;

#calculation:
d  =  e0*er*A/C

#Results
print  "\n\nResult\n\n"
print  "\n  Thickness    ",(d/1E-3),"  mm\n"


Result



  Thickness     0.4   mm

Example 9, page no. 62

In [11]:
from __future__ import division
import math
#initializing  the  variables:
n  =  19;#  no.  of  plates
L  =  75E-3;#  in  m
B  =  75E-3;#  in  m
d  =  0.2E-3;#  in  m
e0  =  8.85E-12;#  in  F/m
er  =  5;
#calculation:
A  =  L*B
C  =  e0*er*A*(n-1)/d

#Results
print  "\n\nResult\n\n"
print  "\n  Capacitance  ",round((C/1E-9),2),"  nF\n"


Result



  Capacitance   22.4   nF

Example 10, page no. 65

In [12]:
from __future__ import division
import math
#initializing  the  variables:
C1  =  6E-6;#  in  Farads
C2  =  4E-6;#  in  Farads

#calculation:
#  in  Parallel
Cp  =  C1 + C2
#  in  Series
Cs  =  1/((1/C1)  +  (1/C2))

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Capacitance  in  parallel  ",(Cp/1E-6),"  uF\n"
print  "\n  (b)Capacitance  in  Series  ",(Cs/1E-6),"  uF\n"


Result



  (a)Capacitance  in  parallel   10.0   uF


  (b)Capacitance  in  Series   2.4   uF

Example 11, page no. 65

In [13]:
from __future__ import division
import math
#initializing  the  variables:
C1  =  30E-6;#  in  Farads
Cs  =  12E-6;#  in  Farads

#calculation:
#  in  Series
C2  =  1/((1/Cs)  -  (1/C1))

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Capacitance  in  series  ",(C2/1E-6),"  uF\n"


Result



  (a)Capacitance  in  series   20.0   uF

Example 12, page no. 65

In [7]:
from __future__ import division
import math
#initializing  the  variables:
C1  =  1E-6;#  in  Farads
C2  =  3E-6;#  in  Farads
C3  =  5E-6;#  in  Farads
C4  =  6E-6;#  in  Farads
Vt  =  100;#  in  Volts

#calculation:
#  in  Parallel
Cp  =  C1  +  C2  +  C3  +  C4
Qt  =  Vt*Cp
Q1  =  C1*Vt
Q2  =  C2*Vt
Q3  =  C3*Vt
Q4  =  C4*Vt

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Equivalent  Capacitance  in  Parallel  ",(Cp/1E-6),"  uF\n"
print  "\n  (b)Total  charge  ",(Qt/1E-3),"  mC\n"
print  "\n  (c)Charge  on  each  capacitors  (C1,  C2,  C3,  C4)\n    ",(Q1/1E-3),", ",(Q2/1E-3),", ",(Q3/1E-3),",",(Q4/1E-3)," mC  respectively\n"


Result



  (a)Equivalent  Capacitance  in  Parallel   15.0   uF


  (b)Total  charge   1.5   mC


  (c)Charge  on  each  capacitors  (C1,  C2,  C3,  C4)
     0.1 ,  0.3 ,  0.5 , 0.6  mC  respectively

Example 13, page no. 66

In [15]:
from __future__ import division
import math
#initializing  the  variables:
C1  =  3E-6;#  in  Farads
C2  =  6E-6;#  in  Farads
C3  =  12E-6;#  in  Farads
Vt  =  350;#  in  Volts
#calculation:
#  in  series
Cs  =  1/((1/C1)  +  (1/C2)  +  (1/C3))
Qt  =  Vt*Cs
V1  =  Qt/C1
V2  =  Qt/C2
V3  =  Qt/C3

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Equivalent  Capacitance  in  Series  ",(Cs/1E-6),"  uF\n"
print  "\n  (b)Charge  on  each  capacitors  (C1,  C2,  C3)  ",(Qt/1E-3),"  mC  \n"
print  "\n  (b)P.d  Across  each  capacitors  (C1,  C2,  C3)\n   ",V1,"  V,  ",  V2,"  V,  ",  V3,"  V  respectively\n"


Result



  (a)Equivalent  Capacitance  in  Series   1.71428571429   uF


  (b)Charge  on  each  capacitors  (C1,  C2,  C3)   0.6   mC  


  (b)P.d  Across  each  capacitors  (C1,  C2,  C3)
    200.0   V,   100.0   V,   50.0   V  respectively

Example 14, page no. 67

In [16]:
from __future__ import division
import math
#initializing  the  variables:
C  =  0.2E-6;#  in  Farads
V  =  1250;#  in  Volts
E = 50E6#  in  V/m
e0  =  8.85E-12;#  in  F/m
er  =  6;

#calculation:
d  =  V/E
A  =  C*d/e0/er

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Thickness  ",(d/1E-3),"  mm\n"
print  "\n  (b)Area  of  plate  is  ",round((A/1E-4),2),"  cm^2  \n"


Result



  (a)Thickness   0.025   mm


  (b)Area  of  plate  is   941.62   cm^2

Example 15, page no. 68

In [17]:
from __future__ import division
import math
#initializing  the  variables:
C  =  3E-6;#  in  Farads
V  =  400;#  in  Volts
t  =  10E-6;#  in  secs

#calculation:
W  =  C*V*V/2
P  =  W/t

#Results
print  "\n\nResult\n\n"
print  "\n  (a)Energy  stored  ",W,"  J\n"
print  "\n  (b)Power  developed  ",(P/1E3),"  kW  \n"


Result



  (a)Energy  stored   0.24   J


  (b)Power  developed   24.0   kW

Example 16, page no. 68

In [18]:
from __future__ import division
import math
#initializing  the  variables:
C  =  12E-6;#  in  Farads
W  =  4;#  in  Joules

#calculation:
V  =  (2*W/C)**0.5

#Results
print  "\n\nResult\n\n"
print  "\n  P.d  ",round(V,2),"  V\n"


Result



  P.d   816.5   V

Example 17, page no. 68

In [19]:
from __future__ import division
import math
#initializing  the  variables:
W  =  1.2;#  in  Joules
Q  =  10E-3;#  in  Coulomb

#calculation:
V  =  2*W/Q
C  =  Q/V

#Results
print  "\n\nResult\n\n"
print  "\n  (a)P.d  ",V,"  V\n"
print  "\n  (b)Capacitance  ",round((C/1E-6),2),"  uF\n"


Result



  (a)P.d   240.0   V


  (b)Capacitance   41.67   uF