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"source": [
"# CHAPTER 12: INSTRUMENT CALIBRATION"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 12-1, Page Number: 355"
]
},
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"execution_count": 8,
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"text": [
"When scale reading is 10 V and precise voltage is 9.5 V,\n",
"Error=- -5.0 % of reading= -0.5 % of full scale\n",
"\n",
"When scale reading is 50 V and precise voltage is 51.7 V,\n",
"Error= + 3.4 % of reading= + 1.7 % of full scale\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variable Declaration\n",
"\n",
"#For Scale reading =10 V, and precise voltage=9.5 V\n",
"scale_reading=10 #Scale reading is 10 V\n",
"\n",
"precise_reading=9.5 #Precise voltage is 9.5 V\n",
"\n",
"error=(precise_reading-scale_reading)/scale_reading*100 #Error in percentage form w.r.t reading\n",
"\n",
"error_fullscale=(precise_reading-scale_reading)*100/100 #Error with respect to full scale \n",
"\n",
"\n",
"print \"When scale reading is 10 V and precise voltage is 9.5 V,\"\n",
"print \"Error=-\",round(error,1),\"% of reading=\",error_fullscale, \"% of full scale\"\n",
"\n",
"print \n",
"#For Scale reading =50 V, and precise voltage=51.7 V\n",
"scale_reading=50 #Scale reading is 50 V\n",
"precise_reading=51.7 #Precise voltage is 51.7 V\n",
"error=(precise_reading-scale_reading)/scale_reading*100 #Error in percentage form \n",
"error_fullscale=(precise_reading-scale_reading)*100/100\n",
"\n",
"print \"When scale reading is 50 V and precise voltage is 51.7 V,\"\n",
"print \"Error= +\",round(error,1),\"% of reading= +\",error_fullscale, \"% of full scale\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 12-2, Page Number: 357"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Correction figure= -6 W\n",
"Error= -5 %\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variable Declaration\n",
"\n",
"V=114 #Measured Voltage in V\n",
"I=1 #Measured Current in A\n",
"W=120 #Full Scale wattage in W\n",
"\n",
"P=V*I #Wattmeter Power\n",
"error=P-W #Correction figure\n",
"print \"Correction figure=\",error,\"W\"\n",
"\n",
"error=error*100/W #Error %\n",
"\n",
"print \"Error=\",error,\"%\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 12-3, Page Number 361"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Therefore Vo= 5 V ± 700.0 micro volt\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variable Declaration\n",
"\n",
"R4=1125.0\n",
"R5=4017.9\n",
"Vz=6.4\n",
"accuracy=100.0/10**6 #100ppm\n",
"\n",
"#Calculation\n",
"#Maximum and Minimum values of resistances in ohm\n",
"R4max=R4*(1+accuracy) \n",
"R4min=R4*(1-accuracy)\n",
"R5max=R5*(1+accuracy)\n",
"R5min=R5*(1-accuracy)\n",
"\n",
"#Maximum and minimum zener voltages in V\n",
"Vzmax=Vz+Vz*0.01/100 #Maximum voltage is Vz+0.01% of Vz\n",
"Vzmin=Vz-Vz*0.01/100 #Minimum voltage is Vz-0.01% of Vz\n",
"\n",
"#Maximum and minimum output voltages in V\n",
"Vomax=Vzmax*(R5max/(R4min+R5max)) #Output is maximum when Vz is maximum, R5 is minimum and R4 is maximum\n",
"Vomin=Vzmin*(R5min/(R4max+R5min)) #Output is minimum when Vzi mimimum, R5 is maximum and R4 is minimum\n",
"Vo=Vz*(R5/(R4+R5))\n",
"\n",
"error=round(Vomax-Vo,4) #Deviation of output voltage from theoretical value \n",
"\n",
"#Result\n",
"print \"Therefore Vo=\",int(Vo),\"V ±\",error*10**6,\"micro volt\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Example 12-4, Page Number: 364"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"When the potentiometer is calibrated, I= 20.0 mA\n",
"R1= 50.0 ohm\n",
"\n",
"Vx= 1.886 V\n",
"\n",
"The value of R2 to limit standard cell current to 20 micro ampere is 200 kilo ohm\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variable Declaration\n",
"\n",
"Rab=100 #Resistance of wire AB, in ohm\n",
"Vb1=3 #Battery B1, terminal voltage(V)\n",
"Vb2=1.0190 #Standard Cell Voltage(V) \n",
"l=50.95 #Length BC, in cm\n",
"\n",
"#At Calibration\n",
"\n",
"Vbc=Vb2 \n",
"volt_per_unit_length=Vbc/l #in V/cm\n",
"Vab=100*volt_per_unit_length #in V \n",
"I=Vab/Rab #Ohm's Law\n",
"Vr1=Vb1-Vab #KVL \n",
"R1=Vr1/I \n",
"\n",
"#At 94.3cm\n",
"Vx=94.3*volt_per_unit_length\n",
"\n",
"#Worst case: Terminal voltage of B2 or B1 may be reversed\n",
"#Total voltage producing current flow through standard cell is\n",
"\n",
"Vt=Vb2+Vb1\n",
"R2=Vt/(20*10**-6) #Value of resistance R2 to limit standard cell current to a maximum of 20 micro ampere\n",
"\n",
"\n",
"print \"When the potentiometer is calibrated, I=\",I*10**3,\"mA\"\n",
"print \"R1=\",R1,\"ohm\"\n",
"\n",
"print \n",
"print \"Vx=\",round(Vx,3),\"V\"\n",
"print \n",
"print \"The value of R2 to limit standard cell current to 20 micro ampere is \",int(R2*10**-3),\"kilo ohm\""
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Example 12-5, Page Number: 367"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The instrument can measure a maximum of 1.6 V\n",
"Instrument resolution=± 0.2 mV\n"
]
}
],
"source": [
"import math\n",
"\n",
"R3=509.5 #in ohm\n",
"R4=290.5 #in ohm\n",
"R13=100 #in ohm\n",
"l=100 #in cm\n",
"Vb2=1.0190 #in V(Standard Cell Voltage)\n",
"\n",
"Vr3=Vb2 \n",
"I1=Vb2/R3 #Ohm's Law \n",
" \n",
"#Maximum measurable voltage:\n",
"Vae=I1*(R3+R4) #Maximum measurable voltage in V\n",
"\n",
"#Resolution\n",
"I2=Vae/(8*R13) #in A \n",
"\n",
"Vab=I2*R13\n",
"slidewire_vper_length=Vab/l #in V/mm\n",
"\n",
"instrument_resolution=slidewire_vper_length*1 #As contact can be read within 1 mm, 1 is multiplied\n",
"\n",
"print \"The instrument can measure a maximum of\",Vae,\"V\"\n",
"print \"Instrument resolution=±\",instrument_resolution*10**2,\"mV\""
]
}
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