# Chapter 10: Electrical measuring instruments and measurements

### Example 1, page no. 116

In :
from __future__ import division
import math
#initializing  the  variables:
Ia  =  0.040;#  in  Amperes
I  =  50;#  in  Amperes
ra  =  25;#  in  ohms

#calculation:
Is  =  I  -  Ia
V  =  Ia*ra
Rs  =  V/Is

#Results
print  "\n\n  Result  \n\n"
print  "\n    value  of  the  shunt  to  be  connected  in  parallel  =  ",  round((Rs/1E-3),2),"  mohms\n"


Result

value  of  the  shunt  to  be  connected  in  parallel  =   20.02   mohms

### Example 2, page no. 116

In :
from __future__ import division
import math
#initializing  the  variables:
V  =  100;#  in  volts
I  =  0.008;#  in  Amperes
ra  =  10;#  in  ohms

#calculation:
Rm  =  (V/I)  -  ra

#Results
print  "\n\n  Result  \n\n"
print  "\n  value  of  the  multiplier  to  be  connected  in  series  =  ",  (Rm/1E3),"  kohms\n"


Result

value  of  the  multiplier  to  be  connected  in  series  =   12.49   kohms

### Example 3, page no. 119

In :
from __future__ import division
import math
#initializing  the  variables:
fsd  =  200;#  in  volts
R1  =  250;#  in  ohms
R2  =  2E6;#  in  ohms
sensitivity  =  10000;#  in  ohms/V
V = 100; # in volts

#calculation:
Rv  =  sensitivity*fsd
Iv  =  V/Rv
Pv  =  V*Iv
I1  =  V/R1
P1  =  V*I1
I2  =  V/R2
P2  =  V*I2

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  power  dissipated  by  the  voltmeter  =  ",  (Pv/1E-3),"  mW\n"
print  "\n  (b)the  power  dissipated  by  resistor  250  ohm  =  ",  P1,"  W\n"
print  "\n  (c)the  power  dissipated  by  resistor  2  Mohm  =  ",  (P2/1E-3),"  mW\n"


Result

(a)the  power  dissipated  by  the  voltmeter  =   5.0   mW

(b)the  power  dissipated  by  resistor  250  ohm  =   40.0   W

(c)the  power  dissipated  by  resistor  2  Mohm  =   5.0   mW

### Example 4, page no. 119

In :
from __future__ import division
import math
#initializing  the  variables:
V  =  10;#  in  volts
fsd  =  0.1;#  in  Amperes
ra  =  50;#  in  ohms
R  =  500;#  in  ohms

#calculation:
Ie  =  V/R
Ia  =  V/(R  +  ra)
Pa  =  Ia*Ia*ra
PR  =  Ia*Ia*R

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)expected  ammeter  reading  =  ",  (Ie/1E-3),"  mA\n"
print  "\n  (b)Actual  ammeter  reading  =  ",round((Ia/1E-3),2),"  mA\n"
print  "\n  (c)Power  dissipated  in  the  ammeter  =  ",round((Pa/1E-3),2),"  mW\n"
print  "\n  (d)Power  dissipated  in  the  load  resistor  =  ",  round((PR/1E-3),2),"  mW\n"


Result

(a)expected  ammeter  reading  =   20.0   mA

(b)Actual  ammeter  reading  =   18.18   mA

(c)Power  dissipated  in  the  ammeter  =   16.53   mW

(d)Power  dissipated  in  the  load  resistor  =   165.29   mW

### Example 5, page no. 120

In :
from __future__ import division
import math
#initializing  the  variables:
fsd  =  100;#  in  volts
R1  =  40E3;#  in  ohms
R2  =  60E3;#  in  ohms
sensitivity  =  1600;#  in  ohms/V

#calculation:
V1  =  (R1/(R1  +  R2))*fsd
Rv  =  fsd*sensitivity
Rep  =  R1*Rv/(R1  +  Rv)
V1n  =  (Rep/(Rep  +  R2))*fsd

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  value  of  voltage  V1  with  the  voltmeter6  not  connected  =  ",  V1,"  V\n"
print  "\n  (b)the  voltage  indicated  by  the  voltmeter  when  connected  between  A  and  B  =  ",round(V1n,2),"  V\n"


Result

(a)the  value  of  voltage  V1  with  the  voltmeter6  not  connected  =   40.0   V

(b)the  voltage  indicated  by  the  voltmeter  when  connected  between  A  and  B  =   34.78   V

### Example 6, page no. 120

In :
from __future__ import division
import math
#initializing  the  variables:
I  =  20;#  in  amperes
R  =  2;#  in  ohms
Rw  =  0.01;#  in  ohms

#calculation:
PR  =  I*I*R
Rt  =  R  +  Rw
Pw  =  I*I*Rt

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  power  dissipated  in  the  load  =  ",  PR,"  W\n"
print  "\n  (b)the  wattmeter  reading.  =  ",Pw,"  W\n"


Result

(a)the  power  dissipated  in  the  load  =   800   W

(b)the  wattmeter  reading.  =   804.0   W

### Example 8, page no. 122

In :
from __future__ import division
import math
#initializing  the  variables:
tc  =  100E-6;#  in  s/cm
Vc  =  20;#  in  V/cm
w  =  5.2;#  in  cm  (  width  of  one  complete  cycle  )
h = 3.6; # in cm ( peak-to-peak height of the display )

#calculation:
T  =  w*tc
f  =  1/T
ptpv  =  h*Vc

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  periodic  time,  T  =  ",  (T/1E-3),"  msec\n"
print  "\n  (b)Frequency,  f  =  ",round(f,2),"  Hz\n"
print  "\n  (c)the  peak-to-peak  voltage  =  ",ptpv,"  V\n"


Result

(a)the  periodic  time,  T  =   0.52   msec

(b)Frequency,  f  =   1923.08   Hz

(c)the  peak-to-peak  voltage  =   72.0   V

### Example 9, page no. 123

In :
from __future__ import division
import math
#initializing  the  variables:
tc  =  50E-3;#  in  s/cm
Vc  =  0.2;#  in  V/cm
w  =  3.5;#  in  cm  (  width  of  one  complete  cycle  )
h = 3.4; # in cm ( peak-to-peak height of the display )

#calculation:
T  =  w*tc
f  =  1/T
ptpv  =  h*Vc

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  periodic  time,  T  =  ",  (T/1E-3),"  msec\n"
print  "\n  (b)Frequency,  f  =  ",round(f,2),"  Hz\n"
print  "\n  (c)the  peak-to-peak  voltage  =  ",ptpv,"  V\n"


Result

(a)the  periodic  time,  T  =   175.0   msec

(b)Frequency,  f  =   5.71   Hz

(c)the  peak-to-peak  voltage  =   0.68   V

### Example 10, page no. 123

In :
from __future__ import division
import math
#initializing  the  variables:
tc  =  500E-6;#  in  s/cm
Vc  =  5;#  in  V/cm
w  =  4;#  in  cm  (  width  of  one  complete  cycle  )
h = 5; # in cm ( peak-to-peak height of the display )

#calculation:
T  =  w*tc
f  =  1/T
ptpv  =  h*Vc
Amp  =  ptpv/2
Vrms  =  Amp/(2**0.5)

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Frequency,  f  =  ",f,"  Hz\n"
print  "\n  (b)the  peak-to-peak  voltage  =  ",ptpv,"  V\n"
print  "\n  (c)Amplitude  =  ",Amp,"  V\n"
print  "\n  (d)r.m.s  voltage  =  ",round(Vrms,2),"  V\n"


Result

(a)Frequency,  f  =   500.0   Hz

(b)the  peak-to-peak  voltage  =   25   V

(c)Amplitude  =   12.5   V

(d)r.m.s  voltage  =   8.84   V

### Example 11, page no. 123

In :
from __future__ import division
import math

#initializing  the  variables:
tc  =  100E-6;#  in  s/cm
Vc  =  2;#  in  V/cm
w  =  5;#  in  cm  (  width  of  one  complete  cycle  for  both  waveform  )
h1 = 2; # in cm ( peak-to-peak height of the display )
h2 = 2.5; # in cm ( peak-to-peak height of the display

#calculation:
T  =  w*tc
f  =  1/T
ptpv1  =  h1*Vc
Vrms1  =  ptpv1/(2**0.5)
ptpv2  =  h2*Vc
Vrms2  =  ptpv2/(2**0.5)
phi  =  0.5*360/w

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Frequency,  f  =  ",f,"  Hz\n"
print  "\n  (b1)r.m.s  voltage  of  1st  waveform  =  ",round(Vrms1,2),"  V\n"
print  "\n  (b2)r.m.s  voltage  of  2nd  waveform  =  ",round(Vrms2,2),"  V\n"
print  "\n  (c)Phase  difference  =  ",phi,"deg\n"


Result

(a)Frequency,  f  =   2000.0   Hz

(b1)r.m.s  voltage  of  1st  waveform  =   2.83   V

(b2)r.m.s  voltage  of  2nd  waveform  =   3.54   V

(c)Phase  difference  =   36.0 deg

### Example 12, page no. 127

In :
from __future__ import division
import math
#initializing  the  variables:
rP1  =  3;#  ratio  of  two  powers
rP2  =  20;#  ratio  of  two  powers
rP3  =  400;#  ratio  of  two  powers
rP4  =  1/20;#  ratio  of  two  powers

#calculation:
X1  =  10*(1/2.303)*math.log(3)
X2  =  10*(1/2.303)*math.log(20)
X3  =  10*(1/2.303)*math.log(400)
X4  =  10*(1/2.303)*math.log(1/20)

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)decibel  power  ratio  for  power  ratio  3  =  ",round(X1,2),"  dB\n"
print  "\n  (b)decibel  power  ratio  for  power  ratio  20  =  ",round(X2,2),"  dB\n"
print  "\n  (c)decibel  power  ratio  for  power  ratio  400  =  ",round(X3,2),"  dB\n"
print  "\n  (d)decibel  power  ratio  for  power  ratio  1/20  =  ",round(X4,2),"  dB\n"


Result

(a)decibel  power  ratio  for  power  ratio  3  =   4.77   dB

(b)decibel  power  ratio  for  power  ratio  20  =   13.01   dB

(c)decibel  power  ratio  for  power  ratio  400  =   26.02   dB

(d)decibel  power  ratio  for  power  ratio  1/20  =   -13.01   dB

### Example 13, page no. 127

In :
from __future__ import division
import math
#initializing  the  variables:
I2  =  0.020;#  in  ampere
I1  =  0.005;#  in  ampere

#calculation:
X  =  20*math.log10(math.e)*math.log(I2/I1)

#Results
print  "\n\n  Result  \n\n"
print  "\n  decibel  current  ratio  =  ",round(X,2),"  dB\n"


Result

decibel  current  ratio  =   12.04   dB


### Example 14, page no. 128

In :
from __future__ import division
import math
#initializing  the  variables:
rP  =  0.06;#  power  ratios  rP  =  P2/P1

#calculation:
X  =  10*math.log10(math.e)*math.log(rP)

#Results
print  "\n\n  Result  \n\n"
print  "\n  decibel  Power  ratios  =  ",round(X,2),"  dB\n"


Result

decibel  Power  ratios  =   -12.22   dB


### Example 15, page no. 128

In :
from __future__ import division
import math
#initializing  the  variables:
X  =  14;#  decibal  power  ratio  in  dB
P1  =  0.008;#  in  Watt

#calculation:
rP  =  10**(X/10)
P2  =  rP*P1

#Results
print  "\n\n  Result  \n\n"
print  "\n  output  power  P2  =  ",round(P2,2),"  W\n"


Result

output  power  P2  =   0.2   W

### Example 16, page no. 128

In :
from __future__ import division
import math
#initializing  the  variables:
X  =  27;#  Voltage  gain  in  decibels
V2  =  4;#  output  voltage  in  Volts

#calculation:
V1  =  V2/(10**(27/20))

#Results
print  "\n\n  Result  \n\n"
print  "\n  input  Voltage  V1  =  ",round(V1,2),"  V\n"


Result

input  Voltage  V1  =   0.18   V

### Example 17, page no. 129

In :
from __future__ import division
import math
#initializing  the  variables:
R2  =  100;#  in  ohms
R3  =  400;#  in  ohms
R4  =  10;#  in  ohms

#calculation:
R1  =  R2*R3/R4

#Results
print  "\n\n  Result  \n\n"
print  "\n unknown  resistance,  R1  =  ",R1,"  Ohms\n"


Result

unknown  resistance,  R1  =   4000.0   Ohms

### Example 18, page no. 130

In :
from __future__ import division
import math
#initializing  the  variables:
E1  =  1.0186;#  in  Volts
l1  =  0.400;#  in  m
l2  =  0.650;#  in  m

#calculation:
E2  =  (l2/l1)*E1

#Results
print  "\n\n  Result  \n\n"
print  "\n  the  e.m.f.  of  a  dry  cell  =  ",round(E2,2),"  Volts\n"


Result

the  e.m.f.  of  a  dry  cell  =   1.66   Volts

### Example 19, page no. 132

In :
from __future__ import division
import math
#initializing  the  variables:
I  =  0.0025;#  in  Amperes
R  =  5000;#  in  ohms
e1  =  0.4;#  in  %
e2  =  0.5;#  in  %

#calculation:
V  =  I*R
em  =  e1  +  e2
Ve  =  em*V/100

#Results
print  "\n\n  Result  \n\n"
print  "\n  voltage  V  =  ",V,"V(+-)",Ve,"V\n"


Result

voltage  V  =   12.5 V(+-) 0.1125 V

### Example 20, page no. 132

In :
from __future__ import division
import math
#initializing  the  variables:
I  =  6.25;#  in  Amperes
Im  =  10;#  max  in  Amperes
V  =  36.5;#  in  volts
Vm  =  50;#  max  in  volts
e  =  2;#  in  %

#calculation:
R  =  V/I
Ve  =  e*Vm/100
Ve1  =  Ve*100/V#  in    %
Ie  =  e*Im/100
Ie1  =  Ie*100/I#  in  %
em  =  Ve1  +  Ie1
Re  =  em*R/100

#Results
print  "\n\n  Result  \n\n"
print  "\n  Resistance  R  =  ",R,"  ohms(+-)",Re,"  ohms\n"


Result

Resistance  R  =   5.84   ohms(+-) 0.34688   ohms

### Example 21, page no. 133

In :
from __future__ import division
import math
#initializing  the  variables:
R1  =  1000;#  in  ohms
R2  =  100;#  in  ohms
R3  =  432.5;#  in  ohms
e1  =  1;#  in  %
e2  =  0.5;#  in  %
e3  =  0.2;#  in  %

#calculation:
Rx  =  R2*R3/R1
em  =  e1  +  e2  +  e3
Re  =  em*Rx/100

#Results
print  "\n\n  Result  \n\n"
print  "\n  Resistance  R  =  ",Rx,"  ohms(+-)",Re,"  ohms\n"


Result

Resistance  R  =   43.25   ohms(+-) 0.73525   ohms