Chapter 4 Voltmeters and multimeters¶

Example 4.1 Page no 80¶

In :
#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 :
#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 :
#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 :
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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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"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 :
#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 :
#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 :
#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

Example 4.15 Page no 100¶

In :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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