#example 9.1
#calculation of the volume resistivity
from math import pi
#given data
V=1000.#applied voltage(in V)
Rs=10**7#standard resistance(in ohm)
n=3000.#universal shunt ratio
Ds=33.3#deflection(in cm) for Rs
D=3.2#deflection(in cm)
d=10.#diameter(in cm) of the electrodes
t=2*10**-1#thickness(in cm) of the specimen
#calculation
G=V/(Rs*n*Ds)#galvanometer sensitivity
R=V/(D*G)#resistance of the specimen
r=d/2#radius of the electrodes
rho=(pi*r**2*R)/t#volume resistivity
#results
print '%s %.3e' %('The volume resistivity is (ohmcm) = ',rho)
#example 9.2
#calculation of resistivity of the specimen
import math
from math import log
#given data
tm=30.#time (in minute)
ts=20.#time(in second)
Vn=1000.#voltage(in V) to which the condenser was charged
V=500.#voltage(in V) fall to
C=0.1*10**-6#capacitance(in Farad)
d=10.#diameter(in cm) of the electrodes
th=2*10**-1#thickness(in cm) of the specimen
#calculation
t=(tm*60)+ts
R=t/(C*log(Vn/V))#resistance
r=d/2#radius of the electrodes
rho=(math.pi*r**2*R)/th#volume resistivity
#results
print '%s %.3e' %('The resistivity of the specimen is (ohmcm) = ',rho)
#example 9.3
#calculation of dielectric constant and complex permittivity of bakelite
from cmath import pi
#given data
C=147*10**-12#capacitance(in Farad)
Ca=35*10**-12#air capacitance(in Farad)
tandelta=0.0012
epsilon0=(36*pi*10**9)**-1#electrical permittivity(in F/m) of free space
#calculation
epsilonr=C/Ca#dielectric constant
Kdash=epsilonr
Kdashdash=tandelta*Kdash
Kim=complex(Kdash,-Kdashdash)
epsilonast=epsilon0*Kim
print 'The dielectric constant is ',epsilonr
print '%s %.3e %.3e %s' %('The complex permittivity(in F/m)is ',epsilonast.real,epsilonast.imag,'j')
#example 9.4
#calculation of capacitance and tandelta of bushing
from math import pi
#given data
R3=3180.#resistance(in ohm)
R4=636.#resistance(in ohm)
Cs=100.#standard condenser(in pF)
f=50.#frequency(in Hz)
C3=0.00125*10**-6#capacitance(in farad)
#calculation
omega=2*pi*f
Cx=R3*Cs/R4#unknown capacitance
tandelta=omega*C3*R3
#results
print 'The capacitance is (pF) = ',Cx
print '\nThe value of tandelta of bushing is ',round(tandelta,5)
#example 9.5
#calculation of dielectric constant and tandelta of the transformer oil
#given data
f=1*10**3#frequency(in Hz)
C1=504.#capacitance(in pF) for standard condenser and leads
D1=0.0003#dissipation factor for standard condenser and leads
C2=525.#capacitance(in pF) for standard condenser in parallel with the empty test cell
D2=0.00031#dissipation factor for standard condenser in parallel with the empty test cell
C3=550.#capacitance(in pF) for standard condenser in parallel with the test cell and oil
D3=0.00075#dissipation factor for standard condenser in parallel with the test cell and oil
#calculation
Ctc=C2-C1#capacitance of the test cell
Ctcoil=C3-C1#capacitance of the test cell + oil
epsilonr=Ctcoil/Ctc#dielectric constant of oil
deltaDoil=D3-D2#deltaD of oil
#results
print 'The dielectric constant is ',round(epsilonr,2)
print '\nThe value of tandelta of the transformer oil is ',round(deltaDoil,5)
#example 9.6
#calculation of magnitude of the charge transferred from the cavity
from math import pi
#given data
Vd=0.2#discharge voltage(in V)
s=1#sensitivity(in pC/V)
epsilonr=2.5#relative permittivity
epsilon0=(36*pi*10**9)**-1#electrical permittivity(in F/m) of free space
d1=1*10**-2#diameter(in m) of the cylindrical disc
t1=1*10**-2#thickness(in m) of the cylindrical disc
d2=1*10**-3#diameter(in m) of the cylindrical cavity
t2=1*10**-3#thickness(in m) of the cylindrical cavity
#calculation
Dm=Vd*s#discharge magnitude
Ca=epsilon0*(pi*(d2/2)**2)/t2#capacitance of the cavity
Cb=epsilon0*epsilonr*(pi*(d2/2)**2)/(t1-t2)#capacitance
qc=((Ca+Cb)/Cb)*Dm
#results
print 'The charge transferred from the cavity is (pC) = ',round(qc,2)
#example 9.7
#calculation of dielectric constant and loss factor tandelta
from math import pi
#given data
R3=1000./pi#resistance(in ohm) in CD branch
R4=62.#variable resistance(in ohm)
Cs=100.*10**-12#standard capacitance(in F)
epsilon0=8.854*10**-12#electrical permittivity(in F/m) of free space
f=50.#frequency(in Hz)
C3=50.*10**-9#variable capacitor(in F)
d=1.*10**-3#thickness(in m) of sheet
a=100.*10**-4#electrode effective area(in m**2)
#calculation
Cx=R3*Cs/R4
epsilonr=Cx*d/(epsilon0*a)
omega=2*pi*f
tandelta=omega*C3*R3*d
#results
print 'The dielectric constant is ',round(epsilonr,2)
print '\nThe loss factor tandelta is ',round(tandelta,7)
#In equation of tandelta d is multiplied
#example 9.8
#calculation of voltage at balance
from math import pi,sqrt
#given data
V=10000#applied voltage(in V)
R3=1000/pi#resistance(in ohm) in CD branch
R4=62#variable resistance(in ohm)
Cs=100*10**-12#standard capacitance(in F)
f=50#frequency(in Hz)
C3=50*10**-9#variable capacitor(in F)
#calculation
Rx=C3*R4/Cs
Cx=R3*Cs/R4
omega=2*pi*f
zx=complex(Rx,-1/(omega*Cx))
VR4=R4*V/(R4+zx)
MVR4=sqrt((VR4.real)**2+VR4.imag**2)#magnitude
#results
print 'The voltage across AD branch at balance is (V) = ',round(MVR4,1)
#example 9.9
#calculation of maximum and minimum value of capacitance and tandelta
from math import pi
#given data
R3min=100.#minimum value of R3 resistance(in ohm)
R3max=11100.#maximum value of R3 resistance(in ohm)
R4min=100.#minimum value of R4 resistance(in ohm)
R4max=1000.#maximum value of R4 resistance(in ohm)
Cs=100.*10**-12#standard capacitance(in farad)
C3min=1.*10**-9#minimum value of C3 capacitance(in farad)
C3max=1.11*10**-6#maximum value of C3 capacitance(in farad)
f=50.#frequency(in Hz)
#calculation
Cxmax=R3max*Cs/R4min
Cxmin=R3min*Cs/R4max
omega=2*pi*f
tandeltamax=omega*R3max*C3max
tandeltamin=omega*R3min*C3min
#results
print 'The maximum value of capacitance is (nF) = ',round(Cxmax*10**9,1)
print '\nThe minimum value of capacitance is (pF) = ',round(Cxmin*10**12)
print '\nThe maximum value of tandelta is ',round(tandeltamax,2)
print '%s %.2e' %('\nThe minimum value of tandelta is ',tandeltamin)