Chapter 4 Voltmeters and multimeters

Example 4.1 Page no 80

In [5]:
#Given
I=200.0*10**-6                               # A

#calculation
s=(1/I)*10**-3

#Result
print"Sensitivity is ", s,"Kohm/V"

Sensitivity is  5.0 Kohm/V

Example 4.2 (a) Page no 81

In [1]:
#Given
V=10                               #Volt
Im=50.0*10**-6                       #A
Rm=500                             #ohm

#Calculation
R=((V/Im)-Rm)*10**-3

#Result
print"Reading of resistance is ", R,"Kohm"

Reading of resistance is  199.5 Kohm

Example 4.2 (b) Page no 81

In [9]:
#Given
Im=500.0*10**-6                       #A
V=50                                  #Volts
Rm=1*10**3                            #ohm

#Calculation
S=1/Im
Rs=(S*V)-Rm


print"The value of multiplier resistance is ", Rs*10**-3,"K ohm"

The value of multiplier resistance is  99.0 K ohm

Example 4.3 Page no 82

In [24]:
Im=50.0*10**-6                   #A
Rm=500.0                         #ohm
V=20                           #Volts
V1=50                          #volts
V2=100                         #volts

#Calculation
# For range 0-20 V
Rs=V/(Im)-Rm

# for range 0-50 V
Rs1=V1/(Im)-Rm

# for the range of 0-100 V
Rs2=V2/(Im)-Rm

#Result
print"The value of multiplier required for 0-20 V is ", Rs*10**-3,"Kohm"
print"The value of multiplier required for 0-50 V is ", Rs1*10**-3,"Kohm"
print"The value of multiplier required for 0-100 V is ", Rs2*10**-3,"Kohm"

The value of multiplier required for 0-20 V is  399.5 Kohm
The value of multiplier required for 0-50 V is  999.5 Kohm
The value of multiplier required for 0-100 V is  1999.5 Kohm

Example 4.4 Page no 82

In [25]:
#Given
Im=10*10**-3                       #A
Rm=500                             #ohm
V=20                           #Volts
V1=50                          #volts
V2=100                         #volts

#Calculation
# For range 0-20 V
Rs=V/(Im)-Rm

# for range 0-50 V
Rs1=V1/(Im)-Rm

# for the range of 0-100 V
Rs2=V2/(Im)-Rm

#Result
print"The value of multiplier required for 0-20 V is ", Rs*10**-3,"Kohm"
print"The value of multiplier required for 0-50 V is ", Rs1*10**-3,"Kohm"
print"The value of multiplier required for 0-100 V is ", Rs2*10**-3,"Kohm"

The value of multiplier required for 0-20 V is  1.5 Kohm
The value of multiplier required for 0-50 V is  4.5 Kohm
The value of multiplier required for 0-100 V is  9.5 Kohm

Example 4.5 Page no 83

In [39]:
#Given
Im=10.0*10**-3                                #A
Rm=100                                      #ohm
V=5                                         #Volts
V1=50                                       #Volts
V2=100                                      #volts

#Calculation
Rt=V/Im
R3=Rt-Rm
Rt1=V1/Im
R2=Rt1-(R3+Rm)
Rt2=V2/Im
R1=Rt2-(R2+R3+Rm)

#Result
print" R1= ", R1*10**-3,"Kohm","\n R2= ",R2*10**-3,"Kohm","\n R3= ",R3,"ohm"

 R1=  5.0 Kohm 
 R2=  4.5 Kohm 
 R3=  400.0 ohm

Example 4.6 Page no 83

In [10]:
#Given
V=10                                #Volts
I=2.0*10**-3                          #A
Rm=50                                #ohm
V1=50                               #Volts
V2=100                              #Volts
V3=250                              #Volts

#Calculation
Rt=(V/I)
R4=(Rt-Rm)
Rt1=V1/I
R3=Rt1-(R4+Rm)
Rt2=V2/I
R2=Rt2-(R3+R4+Rm)
Rt3=V3/I
R1=Rt3-(R2+R3+R4+Rm)

#Result
print"Resistances are  R1=", R1*10**-3,"Kohm ","\n R2=",R2*10**-3,"Kohm","\n R3=",R3*10**-3,"Kohm","\n R4=",R4,"ohm"

Resistances are  R1= 75.0 Kohm  
 R2= 25.0 Kohm 
 R3= 20.0 Kohm 
 R4= 4950.0 ohm

Example 4.7 Page no 85

In [48]:
#Given
I=200.0*10**-6                               #A
V=50                                         #v
Rm=100                                       #ohm

#Calculation 
S=(1/I)
Rs=((S*V)-Rm)*10**-3

#Result 
print"The value of multiplier resistance is ", Rs,"Kohm"

The value of multiplier resistance is  249.9 Kohm

Example 4.8 Page no 85

In [5]:
#Given
I=50.0*10**-6                                     #A
V=5                                              #Volts
Rm=1000                                          #ohm
V1=10                                             #volts
V2=50

#Calculation
S=1/I
# for 5 volt range
Rs1=((S*V)-Rm)*10**-3

# for 10 volt range 
Rs2=((S*V1)-Rm)*10**-3

# for 50 volt range
Rs3=((S*V2)-Rm)*10**-3
#Result
print"The value of multiplier resistance is ", Rs1,"Kohm"
print"The value of multiplier resistance is ", Rs2,"Kohm"
print"The value of multiplier resistance is ", Rs3,"Kohm"

The value of multiplier resistance is  99.0 Kohm
The value of multiplier resistance is  199.0 Kohm
The value of multiplier resistance is  999.0 Kohm

Example 4.9 Page no 86

In [16]:
#Given
Im=50.0*10**-6                             #A
V=3                                        #volts
V1=10                                      #Volts
V2=30                                      #Volts
Rm=1000                                    #ohm

#Calculation
S=1/Im
Rs=S*V-Rm
Rs1=S*V1-Rm
Rs2=S*V2-Rm

#Result
print"The value of multiplier resistance is ","\n Rs1= ", Rs*10**-3,"Kohm \n Rs2= ",Rs1*10**-3,"Kohm \n Rs3= ",Rs2*10**-3,"Kohm"

The value of multiplier resistance is  
 Rs1=  59.0 Kohm 
 Rs2=  199.0 Kohm 
 Rs3=  599.0 Kohm

Example 4.10 Page no 86

In [30]:
#Given 
Im=20.0*10**-3                               #A
v=100*10**-3                               #volts
I=50000*10**3                               #A
V=500                                       #Volts

Rm=v/Im
Rsh=(Im*Rm)/(I-Im)
Rsh1=(V/Im)-Rm
P=V*Im

#Result
print"(i) Shunt resistance is ", round(Rsh1*10**-3,0),"Kohm"
print"(ii) Power dissipation is ",P,"Watt"

(i) Shunt resistance is  25.0 Kohm
(ii) Power dissipation is  10.0 Watt

Example 4.11 Page no 87

In [39]:
#Given
V=100                                            #Volts
s=1000                                            #ohm/V
R=10.0*10**3                                    #kohm
R1=10.0*10**3                                      #kohm
s2=20000                                          #ohm/V

#Calculation
V2=(R/(R1+R))*V

#case 1
R2=V2*s
Req=(R*R2)/(R+R2)
V1=(Req/(R1+Req))*V

#case 2
R3=V2*s2
Req2=(R1*R3)/(R1+R3)
V12=(Req2/(R1+Req2))*V

#Result
print"(a) voltmeter indicates ", round(V1,2),"V"
print"(b) Voltmeter will read ",round(V12,2),"V"
print"This example shows that a high sensitivity voltmeter Should be used to get accurate reading"

(a) voltmeter indicates  45.45 V
(b) Voltmeter will read  49.75 V
This example shows that a high sensitivity voltmeter Should be used to get accurate reading

Example 4.12 Page no 88

In [60]:
#Given
s=1*10**3                                  #ohm/V
Rm=0.2*10**3                         #ohm
V=10                                 #Volts
s1=20*10**3                           #ohm/volt
Rm1=1.5*10**3                           #ohm
R0=5.0*10**3                              #ohm
R1=25.0*10**3                             #ohm
V1=30                                   #Volt

#Calculation
VRb=(R0/(R1+R0))*V1
Rm2=s*V
Req=(R0*Rm2)/(R0+Rm2)
VRb2=Req/(Req+R1)*V1
Rm3=s1*V
Req2=(R0*Rm3)/(R0+Rm3)
VRb3=(Req2/(R1+Req2))*V1
E1=((VRb-3.33)/VRb)*100
E2=((VRb-VRb3)/VRb)*100

#Result
print"(i) Voltage across Rb without any meter across it ", VRb,"Volt"
print"(ii) Voltage across Rb when the meter 1 is used ", round(VRb2,2),"Volt"
print"(iii) voltage across arb when the meter 2 is used ", round(VRb3,1),"Volts"
print"(iv) Error in voltmeter when meter 1 is used ", E1,"%"
print"     Error in voltmeter when meter 2 is used ",round(E2,0),"%"

(i) Voltage across Rb without any meter across it  5.0 Volt
(ii) Voltage across Rb when the meter 1 is used  3.53 Volt
(iii) voltage across arb when the meter 2 is used  4.9 Volts
(iv) Error in voltmeter when meter 1 is used  33.4 %
     Error in voltmeter when meter 2 is used  2.0 %

Example 4.13 Page no 89

In [90]:
#Given
V1=5.0                          #Volt 
V2=10                         #Volt
V3=30                         #Volt
S=20*10**3                    #ohm/V
Rb=5.0*10**3                    #ohm
Ra=45.0*10**3                   #ohm
V=50                          #Volt

#Calculation
VRb=Rb/(Ra+Rb)*V
Rm=S*V1
Req=(Rm*Rb)/(Rm+Rb)
VRb1=Req/(Ra+Req)*V
E=((V1-VRb1)/V1)*100
Rm1=S*V2
Req1=(Rm1*Rb)/(Rm1+Rb)
VRb2=(Req1/(Req1+Ra))*V
E1=((V1-VRb2)/V1)*100
Rm2=S*V3
Req2=(Rm2*Rb)/(Rm2+Rb)
VRb3=Req2/(Req2+Ra)*V
E2=((V1-VRb3)/V1)*100

#Result
print"(i) Voltage reading with a voltmeter on 5 volt " ,round(VRb1,3),"Volts","\n percent error is ",round(E,2),"%"
print"(ii) Voltage reading with a voltmeter on 10 volt", round(VRb2,2),"Volts","\n percent error is ",round(E1,2),"%"
print"(iii) Voltage reading with a voltmeter on 10 volt", round(VRb3,2),"Volts","\n percent error is ",round(E,2),"%"

(i) Voltage reading with a voltmeter on 5 volt  4.785 Volts 
 percent error is  4.31 %
(ii) Voltage reading with a voltmeter on 10 volt 4.89 Volts 
 percent error is  2.2 %
(iii) Voltage reading with a voltmeter on 10 volt 4.96 Volts 
 percent error is  1.0 %

Example 4.14 Page no 90

In [7]:
#Given
R1=1000                              #ohm
R2=1000.0                             #ohm
R3=1000.0                              #ohm
Rm=100                               #ohm
I=1                                  #A

#Calculation
Rt=(R1)+((R2*R3)/(R2+R3)) 
Im=(((Rt)/(Rt+Rm))*I)*100

#Result
print"Percent reading due to ammeter loading ", round(Im,1),"%"

Percent reading due to ammeter loading  93.8 %

Example 4.15 Page no 100

In [98]:
#Given
I=1.0*10**-3                         #A
Erms=10                              #Volts
V=0.45                               #Volts
Rm=200                               #ohm

#Calculation
S=1/I
R=(S*V*Erms-Rm)*10**-3

#Result
print"Value of multiplier resistance is ", R,"Kohm"

Value of multiplier resistance is  4.3 Kohm

Example 4.16 Page no 101

In [16]:
#Given
Ifsd=100.0*10**-6                           #A
V=0.45                                    #Volts
Rm=500                                    #ohm
Erms=100

#calculation
Sdc=1/Ifsd
Rs=(Sdc*V*100)-Rm
Rs1=((0.45*Erms)/Ifsd)-Rm

#Result
print"The value of multiplier resistance is ", Rs1*10**-3,"ohm"

The value of multiplier resistance is  449.5 ohm

Example 4.17 Page no 102

In [22]:
#Given
Ifsd=100.0*10**-6                              #A
Rm=100                                       #ohm
V=50                                           #Vrms

#Calculation
Sdc=1/Ifsd
Sac=0.9*Sdc
Rs=Sac*V-Rm

#Result
print"The value of multiplier resistance is ", Rs*10**-3,"Kohm"

The value of multiplier resistance is  449.9 Kohm

Example 4.18 Page no 102

In [103]:
#Given
I=1.0*10**-3                                #A
V=10                                 #volts
Rm=250                               #ohm

#Calculation
Sdc=1/I
Sac=0.9*Sdc
R=(Sac*V-Rm)*10**-3

#Result
print"Value of multiplier resistance is ", R,"Kohm"

Value of multiplier resistance is  8.75 Kohm

Example 4.19 Page no 103

In [60]:
#Given
Ifsd=100*10**-6                              #A
V=10.0                                         #Volts
R2=10.0*10**3                                 #ohm
Rm=100*10**3                                #ohm
R1=10.0*10**3                                 #ohm

Sdc=1/Ifsd
Rs=Sdc*V
Req=(R2*Rm)/(R2+Rm)
ER2=Req/(R1+Req)
Shw=0.45*Sdc
Rs1=Shw*V
Req1=(R2*Rs1)/(R2+Rs1)
E=Req1/(R1+Req1)
Sfw=(0.90*Sdc)
Rs2=Sfw*V
Req2=(R2*Rs2)/(R2+Rs2)
E=(Req2/(R1+Req2))*V

#Result
print"Sensitivity is ",Sdc*10**-3,"Kohm/volt"
print"Multiplier resistance is ",Rs*10**-3,"Kohm"
print"The voltage across R2 is ",round(ER2*10**1,2),"Volts"
print"Resistance using Half wave rectifier ",Rs1*10**-3,"Kohm"
print"Voltage by AC voltmeter is ",round(E,2),"Volts"
print"Resistance using full wave rectifier ",Rs2*10**-3,"Kohm"
print"Voltage by DC voltmeter is ",round(E,2),"Volts"

Sensitivity is  10.0 Kohm/volt
Multiplier resistance is  100.0 Kohm
The voltage across R2 is  4.76 Volts
Resistance using Half wave rectifier  45.0 Kohm
Voltage by AC voltmeter is  4.74 Volts
Resistance using full wave rectifier  90.0 Kohm
Voltage by DC voltmeter is  4.74 Volts

Example 4.20 Page no 113

In [13]:
#Given
Im=1*10**-3                        #A
Rm=100                             #ohm
Rh=1*10**3                         #ohm
V=3.0                               #Volts

#Calculation
R1=Rh-(Im*Rm*Rh)/V
R2=(Im*Rm*Rh)/(V-Im*Rh)
V1=3-0.09
R21=(Im*Rm*Rh)/(V1-Im*Rh)

#Result
print"(i) The value of R1= ",round(R1,2),"ohm"," \n    Value of R2= ",round(R2,2),"ohm"
print"(ii) Maximum value of R2 to compensate for a 3% Drop in Battery Voltage ",round(R21,2),"ohm"

(i) The value of R1=  966.67 ohm  
    Value of R2=  50.0 ohm
(ii) Maximum value of R2 to compensate for a 3% Drop in Battery Voltage  52.36 ohm

Example 4.21 Page no 113

In [17]:
#Given
Rh=2000.0                       #ohm
Ifsd=1*10**-3                   #A
Rm=100                        #ohm
V=3.0                            #Volts
V1=2.58                           #Volts

#Calculation
R1=Rh-((Ifsd*Rm*Rh)/V)
R2=(Ifsd*Rm*Rh)/(V-(Ifsd*Rh))
R21=(Ifsd*Rm*Rh)/(V1-(Ifsd*Rh))

#Result
print"(i) The value of R1=",round(R1,1),"Ohm and Value of R2=",R2,"Ohm" 
print"The maximum value of R2 is ",round(R21,2),"ohm"

(i) The value of R1= 1933.3 Ohm and Value of R2= 200.0 Ohm
The maximum value of R2 is  344.83 ohm

Example 4.22 Page no 114

In [40]:
#Given
V=3                      #volts
Im=1.0*10**-3               #A
Rm=100                    #ohm
P=0.2 
P1=0.4
P2=0.5 
P3=0.75
P4=0.9
P5=1

#calculation
Rs=(V/Im)-Rm
Rx=((Rs+Rm)/P)-(Rs+Rm)
Rx1=((Rs+Rm)/P1)-(Rs+Rm)
Rx2=((Rs+Rm)/P2)-(Rs+Rm)
Rx3=((Rs+Rm)/P3)-(Rs+Rm)
Rx4=((Rs+Rm)/P4)-(Rs+Rm)
Rx5=((Rs+Rm)/P5)-(Rs+Rm)

#Result
print"The value of Rs is ",Rs*10**-3,"Kohm"
print"The value of Rx with 20% detection is ",Rx*10**-3,"Kohm"
print"The value of Rx with 40% detection is ",Rx1*10**-3,"Kohm"
print"The value of Rx with 50% detection is ",Rx2*10**-3,"Kohm"
print"The value of Rx with 75% detection is ",Rx3*10**-3,"Kohm"
print"The value of Rx with 90% detection is ",round(Rx4*10**-3,3),"Kohm"
print"The value of Rx with 100% detection is ",Rx5*10**-3,"Kohm"

The value of Rs is  2.9 Kohm
The value of Rx with 20% detection is  12.0 Kohm
The value of Rx with 40% detection is  4.5 Kohm
The value of Rx with 50% detection is  3.0 Kohm
The value of Rx with 75% detection is  1.0 Kohm
The value of Rx with 90% detection is  0.333 Kohm
The value of Rx with 100% detection is  0.0 Kohm

Example 4.23 Page no 115

In [47]:
#Given
V=3.0                       #Volts
I=1.0*10**-3                #A
V1=2.8

#Calculation
Rt=V/I
Rt1=V1/I
E=((V-V1)/V)*100

#Result
print"The resulting error is ", round(E,2),"%"

The resulting error is  6.67 %

Example 4.24 Page no 116

In [72]:
#Given
Im=1*10**-3                    #A
Rm=100.0                         #ohm
Rh=2000                        #ohm
V=3.0                            #Volts
V1=2.7                            #Volts
V2=3.1                            #Volts

#Calculation
R2=(Im*Rh*Rm)/(V-Im*Rh)
R1=Rh-R2*Rm/R2+Rm
R21=(Im*Rh*Rm)/(V1-Im*Rh)
R22=(Im*Rh*Rm)/(V2-Im*Rh)

#Result
print"(i) The value of R1=",R1-66.6,"ohm and the value of R2=",R2,"ohm"
print"(ii) The value of R2 when battery is 2.7 V is ",round(R21,0),"ohm"
print"     The value of R2 when battery is 3.1 V is ",round(R22,0),"ohm"

(i) The value of R1= 1933.4 ohm and the value of R2= 200.0 ohm
(ii) The value of R2 when battery is 2.7 V is  286.0 ohm
     The value of R2 when battery is 3.1 V is  182.0 ohm

Example 4.25 Page no 118

In [93]:
#Given
I=0.5                          #mA
Im=10                          #mA
Rm=50                          #ohm
Rh=10.0                          #ohm
V=3                              #Volts

#Calculation
Ih=I*Im
Vm=Ih*Rm
Ix=Vm/Rh
Ish=Ix-Ih
Rsh=Vm/Ish
It=Ix+Ih+Ish
V1=V-Vm*10**-3
R1=V1/It

#Result
print"(i) The value of shunt resistance is ", Rsh,"ohm"
print"(ii) Value of current limiting resistance is ", R1*10**3,"ohm"

(i) The value of shunt resistance is  12.5 ohm
(ii) Value of current limiting resistance is  55.0 ohm

Example 4.26 Page no 119

In [114]:
#Given
I=3
R1=10.0                   #ohm
R2=20.0                    #ohm
R3=30.0*10**3                #ohm
R11=100.0                  #ohm
R22=200.0                   #ohm
R12=1000                    #ohm
R21=2000.0                   #ohm

V=I*(R1/(R1+R2))
Im=V/R3
V1=I*(R11/(R11+R22))
Im1=V1/R3
V2=I*(R12/(R12+R21))
Im2=V2/R3
print"(a) Current through the micrometer is ", round(Im*10**6,1),"micro A"
print"(b) The current flows through the meter movement when a 200 ohm resistor is measured ",round (Im1*10**6,1),"micro A"
print"(b) The current flows through the meter movement when a 2 Kohm resistor is measured",round (Im1*10**6,1),"micro A" 

(a) Current through the micrometer is  33.3 micro A
(b) The current flows through the meter movement when a 200 ohm resistor is measured  33.3 micro A
(b) The current flows through the meter movement when a 2 Kohm resistor is measured 33.3 micro A