# CHAPTER 22: ELECTRONIC INSTRUMENTS¶

## Example 22.1 : Page number 606¶

In :
#Variable declaration
I_g=1;                  #Full scale deflection current, mA

#Calculation
MS=1/(I_g/1000.0);        #Multimeter sensitivity, Ω per volt

#Result
print("The multimeter sensitivity=%d Ω per volt."%MS);

The multimeter sensitivity=1000 Ω per volt.


## Example 22.2 : Page number 606-607¶

In :
#Variable declaration
meter_sensitivity=1000.0;                  #Meter sensitivity, Ω per volt
V_full_scale=50.0;                        #Full scale volts
R=50000.0;                                #Resistance to be measured, Ω

#Calculation
meter_resistance=V_full_scale*meter_sensitivity;            #Meter resistance, Ω
R_p=R*meter_resistance/(R+meter_resistance);                #Parallel resistance, Ω

#Result
print("When the meter is used to measure the voltage across the resistance %dΩ, total resistance =%dΩ."%(R,R_p));
print("∴ Meter will give highly incorrect reading.");

When the meter is used to measure the voltage across the resistance 50000Ω, total resistance =25000Ω.
∴ Meter will give highly incorrect reading.


## Example 22.3 : Page number 607¶

In :
#Variable declaration
meter_sensitivity=4.0;                #Meter sensitivity, kΩ/V
R_1=10.0;                             #Resistance across which voltage is to be measured, kΩ
R_2=10.0;                             #Resistance, kΩ
range_max=10.0;                       #Maximum range of the meter, V
range_min=0;                        #Minimum range of the meter, V
V=20.0;                               #Battery voltage, V

#Calculation
R_meter=meter_sensitivity*range_max;                       #Resistance of the meter, kΩ
R_T=(R_meter*R_1)/(R_1+R_meter) +  R_2;                     #Total circuit resistance, kΩ
I_circuit=round(V/R_T,2);                                            #Circuit current, mA
V_multimeter=I_circuit*((R_meter*R_1)/(R_1+R_meter));       #Voltage read by multimeter, V

#Result

Voltage read by multimeter=8.88V.


## Example 22.4 : Page number 607-608¶

In :
#Variable declaration
meter_sensitivity=20.0;                #Meter sensitivity, kΩ/V
R_1=10.0;                             #Resistance across which voltage is to be measured, kΩ
R_2=10.0;                             #Resistance, kΩ
range_max=10.0;                       #Maximum range of the meter, V
range_min=0;                        #Minimum range of the meter, V
V=20.0;                               #Battery voltage, V

#Calculation
R_meter=meter_sensitivity*range_max;                       #Resistance of the meter, kΩ
R_T=round((R_meter*R_1)/(R_1+R_meter) +  R_2,1);                     #Total circuit resistance, kΩ
I_circuit=round(V/R_T,2);                                           #Circuit current, mA
V_multimeter=I_circuit*((R_meter*R_1)/(R_1+R_meter));       #Voltage read by multimeter, V

#Result

#Note: The circuit current=1.0256mA, has been approximated in the text  as 1.04mA. But, in the code 1.03 mA has been used. Therefore, the final answer is obtained as 9.81V and not 9.88V.

Voltage read by multimeter=9.81V.


## Example 22.5 : Page number 608-609¶

In :
from math import floor

#Variable declaration
R_A=20.0;             #Resistance after point A, kΩ
R_B=20.0;             #Resistance after point B, kΩ
R_C=30.0;             #Resistance after point C, kΩ
R_D=30.0;             #Resistance after point D, kΩ
R_meter=60.0;         #Resistance of the meter, kΩ
V=100.0;              #Battery voltage, V

#Calculation
#(i) When meter is not connected:
R_T=R_A+R_B+R_C+R_D;                    #Total circuit resistance, kΩ
I_circuit=V/R_T;                        #Circuit current, mA
V_A=V;                                  #Voltage at point A, V
V_B=V-(I_circuit*R_A);                  #Voltage at point B, V
V_C=V-(I_circuit*(R_A+R_B));            #Voltage at point C, V
V_D=V-(I_circuit*(R_T-R_D));            #Voltage at point D, V

print("(i) When meter is not connected:");
print("    Voltage at point A=%dV."%V_A);
print("    Voltage at point B=%dV."%V_B);
print("    Voltage at point C=%dV."%V_C);
print("    Voltage at point D=%dV."%V_D);

#(ii) When meter is connected:
#(a) Since, point A is directly connected to the source, voltage at point A is equal to source voltage.
V_A=V;                                      #Voltage at point A, V

#(b)
R_T_B=R_A  + round((R_T-R_A)*R_meter/(R_meter + (R_T-R_A)),2);             #Total circuit resistance, kΩ
I_circuit=round(V/R_T_B,2);                                                #Circuit current, mA
V_B=I_circuit*(R_T-R_A)*R_meter/(R_meter + (R_T-R_A));                   #Voltage at point B, V

#(c)
R_T_C=(R_A+R_B)  + (R_T-R_A-R_B)*R_meter/(R_meter + (R_T-R_A-R_B));               #Total circuit resistance, kΩ
I_circuit=V/R_T_C;                                                                #Circuit current, mA
V_C=floor((I_circuit*(R_T-R_A-R_B)*R_meter/(R_meter + (R_T-R_A-R_B)))*10)/10;     #Voltage at point C, V

#(c)
R_T_D=(R_T-R_D)  + R_D*R_meter/(R_meter + R_D);             #Total circuit resistance, kΩ
I_circuit=round(V/R_T_D,2);                                 #Circuit current, mA
V_D=I_circuit*(R_D*R_meter)/(R_meter + R_D);                #Voltage at point D, V

print("(ii) When meter is connected:");
print("     Voltage at point A=%dV."%V_A);
print("     Voltage at point B=%dV."%V_B);
print("     Voltage at point C=%.1fV."%V_C);
print("     Voltage at point D=%.1fV."%V_D);

(i) When meter is not connected:
Voltage at point A=100V.
Voltage at point B=80V.
Voltage at point C=60V.
Voltage at point D=30V.
(ii) When meter is connected:
Voltage at point A=100V.
Voltage at point B=63V.
Voltage at point C=42.8V.
Voltage at point D=22.2V.


## Example 22.6 : Page number 614¶

In :
#Variable declaration
VCC=12.0;                     #Supply voltage, V
R_m=1.0;                      #Meter resistance, kΩ
I_m_fsd=2.0;                  #Full scale deflection of meter current, mA
beta=80.0;                    #Base current amplification factor
E=5.0;                        #Voltage to be measured, V
V_BE=0.7;                   #Base-emitter voltage, V

#Calculation
V_E=E-V_BE;                 #Emitter voltage, V

#(i)
#I_m_fsd=V_E/(R_s+R_m), (OHM's LAW)
R_s=((V_E/I_m_fsd)-R_m)*1000;                  #Multiplier resistor, Ω

#(ii)
IB=I_m_fsd/beta;     				#Base current, mA
R_i=E/IB;                    			#Input resistance of voltmeter, kΩ

#Result
print("(i)  The multiplier resistor=%dΩ."%R_s);
print("(ii) The voltmeter input resistance=%dkΩ"%R_i);

(i)  The multiplier resistor=1150Ω.
(ii) The voltmeter input resistance=200kΩ


## Example 22.7 : Page number 614¶

In :
#Variable declaration
VCC=20;                     #Supply voltage, V
Rs_Rm=9.3;                  #Sum of multipier resistance and meter resistance, kΩ
I_m=1;                      #Meter current, mA
beta=100;                   #Base current amplification factor
E=10;                       #Voltage to be measured, V
V_BE=0.7;                   #Base-emitter voltage, V

#Calculation
#(i)
V_E=E-V_BE;             #Emitter voltage, V
I_m=V_E/Rs_Rm;          #Meter current, mA

#(ii)
I_B=I_m/beta;               #Base current, mA
R_i_T=(E/I_B)/1000;         #Input resistance of voltmeter, with transistor, MΩ
R_i_WT=Rs_Rm;               #Input resistance of voltmeter, without transistor, kΩ

#Result
print("(i) The meter current=%dmA"%I_m);
print("(ii) The input resistance of voltmeter with transistor=%dMΩ."%R_i_T);
print("     The input resistance of voltmeter without transistor=%.1fkΩ."%R_i_WT);

(i) The meter current=1mA
(ii) The input resistance of voltmeter with transistor=1MΩ.
The input resistance of voltmeter without transistor=9.3kΩ.


## Example 22.8 : Page number 614-615¶

In :
#Variable declaration
VCC=20;                     #Supply voltage, V
Rs_Rm=9.3;                  #Sum of multipier resistance and meter resistance, kΩ
I_m=1;                      #Meter current, mA
beta=100;                   #Base current amplification factor
E=5;                        #Voltage to be measured, V
V_BE=0.7;                   #Base-emitter voltage, V

#Calculation
I_m=(E-V_BE)/Rs_Rm;          #Meter current, mA

#Result
print("The meter current=%.2fmA"%I_m);

The meter current=0.46mA


## Example 22.9 : Page number 616¶

In :
from math import sqrt
from math import floor

#Variable declaration
I_m_fsd=100.0;                  #Full scale deflection of meter current, μA
R_m=1.0;                        #Meter resistance, kΩ
V_rms=100.0;                    #r.m.s voltage to be measured, V
V_F=0.7;                      #Forward voltage drop of rectifier diode, V

#Calculation
V_m=round(sqrt(2)*V_rms,1);                                                          #Peak value of applied voltage, V
V_rectifier_drop=2*V_F;                                                              #Total rectifier drop, V
I_peak=round(I_m_fsd/0.637,2);                                                       #Peak f.s.d current, μA
R_s=floor(((((V_m-V_rectifier_drop)/(I_peak*10**-6))-(R_m*1000))/1000)*10)/10;       #Multiplier resistance, kΩ (OHM's LAW)

#Result
print("The multiplier resistance=%.1fkΩ."%R_s);

The multiplier resistance=890.7kΩ.


## Example 22.10 : Page number 616¶

In :
from math import sqrt

#Variable declaration
I_av=75;                  #Full scale deflection of meter current, μA
R_s=708;                     #Multiplier resistor, kΩ
R_m=900;                     #Meter coil resistor, Ω

#Calculation
I_peak=I_av*10**-6/0.637;                   #Peak f.s.d meter current, A
R_T=R_s*1000+R_m;                                #Total circuit resistance, Ω

#I_peak=(Vm-V_drop)/R_T; (OHM's LAW)
#And, Vm=sqrt(2)*Vrms
V_rms=(I_peak*R_T+(2*0.7))/sqrt(2) ;             #applied r.m.s voltage, V

#Result
print("The applied r.m.s voltage=%dV"%V_rms);

The applied r.m.s voltage=60V


## Example 22.11 : Page number 618¶

In :
#Variable declaration
deflection_sensitivity=0.01;            #Deflection sensitivity, mm/V
V=400;                                  #Applied voltage, V

#Calculation
spot_shift=V*deflection_sensitivity;         #Spot shift produced, mm

#Result
print("The shift produced in the spot=%dmm."%spot_shift);

The shift produced in the spot=4mm.


## Example 22.12 : Page number 618-619¶

In :
#Variable declaration
deflection_sensitivity=0.03;            #Deflection sensitivity, mm/V
spot_shift=3;                           #Spot shift produced, mm

#Calculation
#Since, spot_shift=Applied_Voltage*deflection_sensitivity,
V=spot_shift/deflection_sensitivity;    #Applied voltage, V

#Result
print("Applied voltage=%dV."%V);

Applied voltage=100V.


## Example 22.13 : Page number 622¶

In :
#Variable declaration
deflection=2;                            #Deflection produced by applied voltage, cm
V=200;                                   #Applied voltage, V
deflection_by_another_voltage=3;         #Deflection by another voltage, cm

#Calculation
deflection_sensitivity=V/deflection;                                #deflection sensitivity, V/cm
V_unknown=deflection_sensitivity*deflection_by_another_voltage;     #Unknown voltage, V

#Result
print("The unknown voltage=%dV."%V_unknown);

The unknown voltage=300V.


## Example 22.14 : Page number 622¶

In :
#Variable declaration
f_H=1000;                   #Frequency applied to horizontal plates, Hz

#Calculation
#(i)
Loops_H=1;                        #Number of loops cut by horizontal line
Loops_V=1;                        #Number of loops cut by vertical line
f_V=f_H*(Loops_H/Loops_V);        #Unknown frequency, Hz

print("(i)   Unknown frequency=%dHz."%f_V);

#(ii)
Loops_H=2;                        #Number of loops cut by horizontal line
Loops_V=1;                        #Number of loops cut by vertical line
f_V=f_H*(Loops_H/Loops_V);        #Unknown frequency, Hz

print("(ii)  Unknown frequency=%dHz."%f_V);

#(iii)
Loops_H=6;                        #Number of loops cut by horizontal line
Loops_V=1;                        #Number of loops cut by vertical line
f_V=f_H*(Loops_H/Loops_V);        #Unknown frequency, Hz

print("(iii) Unknown frequency=%dHz."%f_V);

(i)   Unknown frequency=1000Hz.
(ii)  Unknown frequency=2000Hz.
(iii) Unknown frequency=6000Hz.