# Chapter 9: Non Destructive testing of materials and electrical apparatus¶

## Example 1: pg 395¶

In :
#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
rho=(pi*r**2*R)/t#volume resistivity
#results
print '%s %.3e' %('The volume resistivity is (ohmcm) = ',rho)

The volume resistivity is (ohmcm) =  1.226e+14


## Example 2: pg 395¶

In :
#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
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
rho=(math.pi*r**2*R)/th#volume resistivity
#results
print '%s %.3e' %('The resistivity of the specimen is (ohmcm) = ',rho)

The resistivity of the specimen is (ohmcm) =  1.031e+13


## Example 3: pg 396¶

In :
#example 9.3
#calculation of dielectric constant and complex permittivity of bakelite
from cmath import pi
#given data
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')

The dielectric constant is  4.2
The complex permittivity(in F/m)is  3.714e-11 -4.456e-14 j


## Example 4: pg 396¶

In :
#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)

#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)

The capacitance is (pF) =  500.0

The value of tandelta of bushing is  0.00125


## Example 5: pg 396¶

In :
#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
#results
print 'The dielectric constant is ',round(epsilonr,2)
print '\nThe value of tandelta of the transformer oil is ',round(deltaDoil,5)

The dielectric constant is  2.19

The value of tandelta of the transformer oil is  0.00044


## Example 6: pg 397¶

In :
#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)

The charge transferred from the cavity is (pC) =  0.92


## Example 7: pg 397¶

In :
#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

The dielectric constant is  5.8

The loss factor tandelta is  5e-06


## Example 8: pg 398¶

In :
#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)

The voltage across AD branch at balance is (V) =  0.1


## Example 9: pg 399¶

In :
#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)
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)

The maximum value of capacitance is (nF) =  11.1

The minimum value of capacitance is (pF) =  10.0

The maximum value of tandelta is  3.87

The minimum value of tandelta is  3.14e-05