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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# CHAPTER 3: ELECTROMECHANICAL INSTRUMENTS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example 3-1, Page Number: 37"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Torque= 3e-06 N.m\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "\n",
+ "N=100\n",
+ "B=0.2 #in Tesla\n",
+ "D=1*10**-2 #in m\n",
+ "l=1.5*10**-2 #in m\n",
+ "I=1*10**-3 #in A\n",
+ "\n",
+ "#Calculation of torque\n",
+ "\n",
+ "Td=B*l*I*N*D #Torque equation\n",
+ "\n",
+ "#Result\n",
+ "print \"Torque=\",Td,\" N.m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-2, Page Number: 39"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Voltage Sensitivity= 1 mV/mm\n",
+ "Megaohm Sensitivity= 1 mega ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "\n",
+ "current_sensitivity=1*10**-6 #in A/mm\n",
+ "damping_resistance=1*10**3 #in ohm\n",
+ "\n",
+ "#Voltage sensitivity\n",
+ "voltage_sensitivity=damping_resistance*current_sensitivity\n",
+ "\n",
+ "#Megaohm sensitivity\n",
+ "\n",
+ "megaohm_sensitivity=1/current_sensitivity\n",
+ "\n",
+ "#Results\n",
+ "print \"Voltage Sensitivity=\",int(voltage_sensitivity*1000),\" mV/mm\"\n",
+ "print \"Megaohm Sensitivity=\",int(megaohm_sensitivity/10**6),\"mega ohm\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-3, Page Number: 41"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "At FSD,\n",
+ "Meter Voltage= 9.9 mV\n",
+ "Meter Current= 0.1 mA\n",
+ "Shunt Current= 9.9 mA\n",
+ "Total Current= 10.0 mA\n",
+ " \n",
+ "At 0.5 FSD,\n",
+ "Meter Voltage= 4.95 mV\n",
+ "Meter Current= 0.05 mA\n",
+ "Shunt Current= 4.95 mA\n",
+ "Total Current= 5.0 mA\n",
+ " \n",
+ "At 0.25 FSD,\n",
+ "Meter Voltage= 2.475 mV\n",
+ "Meter Current= 0.025 mA\n",
+ "Shunt Current= 2.475 mA\n",
+ "Total Current= 2.5 mA\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Rm=99 #Coil resistance in ohm\n",
+ "Im1=0.1*10**-3 #FSD current in A\n",
+ "Rs=1 #Shunt resistance in ohm\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#At FSD\n",
+ "\n",
+ "Vm1=Im1*Rm #Meter Voltage\n",
+ "Is1=Vm1/Rs\n",
+ "It1=Is1+Im1 #Total Current\n",
+ "\n",
+ "#At 0.5 FSD\n",
+ "Im2=0.5*Im1 #0.5 FSD current\n",
+ "Vm2=Im2*Rm #Meter Voltage\n",
+ "Is2=Vm2/Rs #Shunt current\n",
+ "It2=Im2+Is2 #Total current\n",
+ "\n",
+ "\n",
+ "#At 0.25 FSD\n",
+ "Im3=0.25*Im1 #0.25 FSD current\n",
+ "Vm3=Im3*Rm #Meter Voltage\n",
+ "Is3=Vm3/Rs #Shunt current\n",
+ "It3=Im3+Is3 #Total current\n",
+ "\n",
+ "#Results\n",
+ "print \"At FSD,\"\n",
+ "print \"Meter Voltage=\",round(Vm1*1000,1),\" mV\"\n",
+ "print \"Meter Current=\",round(Im1*1000,1),\" mA\"\n",
+ "print \"Shunt Current=\",round(Is1*1000,1),\" mA\"\n",
+ "print \"Total Current=\",round(It1*1000,1),\"mA\"\n",
+ "\n",
+ "print \" \"\n",
+ "print \"At 0.5 FSD,\"\n",
+ "print \"Meter Voltage=\",round(Vm2*1000,2),\" mV\"\n",
+ "print \"Meter Current=\",round(Im2*1000,2),\" mA\"\n",
+ "print \"Shunt Current=\",round(Is2*1000,2),\" mA\"\n",
+ "print \"Total Current=\",round(It2*1000,2),\" mA\"\n",
+ "\n",
+ "print \" \"\n",
+ "print \"At 0.25 FSD,\"\n",
+ "print \"Meter Voltage=\",round(Vm3*1000,3),\" mV\"\n",
+ "print \"Meter Current=\",round(Im3*1000,3),\" mA\"\n",
+ "print \"Shunt Current=\",round(Is3*1000,3),\" mA\"\n",
+ "print \"Total Current=\",round(It3*1000,1),\" mA\"\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-4, Page Number: 43"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "For FSD=100mA,\n",
+ "Shunt Resistance= 1.001 ohm\n",
+ "For FSD=1A,\n",
+ "Shunt Resistance= 0.10001 ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "Im=100*10**-6 #FSD Current in A\n",
+ "Rm=1*10**3 #Coil Resistance \n",
+ "I1=100*10**-3 #Required FSD current\n",
+ "I2=1 #Required FSD current\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#FSD=100mA\n",
+ "Vm1=Im*Rm #Meter Voltage\n",
+ "Is1=I1-Im #Shunt Current\n",
+ "Rs1=Vm1/Is1 #Shunt Resistance\n",
+ "\n",
+ "#FSD=1A\n",
+ "Vm2=Im*Rm #Meter Voltage\n",
+ "Is2=I2-Im #Shunt Current\n",
+ "Rs2=Vm2/Is2 #Shunt Resistance\n",
+ "\n",
+ "#Results\n",
+ "print \"For FSD=100mA,\"\n",
+ "print \"Shunt Resistance=\",round(Rs1,3),\" ohm\"\n",
+ "\n",
+ "print \"For FSD=1A,\"\n",
+ "print \"Shunt Resistance=\",round(Rs2,5),\" ohm\"\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-5, Page Number: 45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "When switch is at B, Ammeter Range= 10 mA\n",
+ "When switch is at C, Ammeter Range= 100 mA\n",
+ "When switch is at D, Ammeter Range= 1 A\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "\n",
+ "R1=0.05 #in ohm\n",
+ "R2=0.45 #in ohm\n",
+ "R3=4.5 #in ohm\n",
+ "Rm=1*10**3 #in ohm\n",
+ "Im=50*10**-6 #in A\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Switch at contact B\n",
+ "Vs1=Im*Rm\n",
+ "Is1=Vs1/(R1+R2+R3)\n",
+ "It1=Im+Is1\n",
+ "\n",
+ "#Switch at contact C\n",
+ "\n",
+ "Vs2=Im*(Rm+R3)\n",
+ "Is2=Vs2/(R1+R2)\n",
+ "It2=Im+Is2\n",
+ "\n",
+ "#Swithc at contact D\n",
+ "\n",
+ "Vs3=Im*(Rm+R3+R2)\n",
+ "Is3=Vs3/R1\n",
+ "It3=Im+Is3\n",
+ "\n",
+ "#Results\n",
+ "print \"When switch is at B, Ammeter Range=\",int(It1*1000),\" mA\"\n",
+ "print \"When switch is at C, Ammeter Range=\",int(It2*1000),\" mA\"\n",
+ "print \"When switch is at D, Ammeter Range=\",int(It3),\" A\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-6, Page Number:47"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "For 50V at full scale, multiplier resistance should be 499 kilo ohm\n",
+ "When instrument reads 0.8 FSD, applied voltage is 40 volt\n",
+ "When instrument reads 0.5 FSD, applied voltage is 25 volt\n",
+ "When instrument reads 0.2 FSD, applied voltage is 10 volt\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Im=100*10**-6 #in A\n",
+ "Rm=1*10**3 #in ohm\n",
+ "V=50 #in V \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "Rs=V/Im-Rm #in ohm \n",
+ "\n",
+ "#At 0.8 FSD\n",
+ "\n",
+ "Im1=0.8*Im #in A\n",
+ "V1=Im1*(Rs+Rm) #in V \n",
+ "\n",
+ "#At 0.5 FSD\n",
+ "Im2=0.5*Im #in A \n",
+ "V2=Im2*(Rs+Rm) #in V \n",
+ "\n",
+ "#At 0.2 FSD\n",
+ "Im3=0.2*Im #in A\n",
+ "V3=Im3*(Rs+Rm) #in V\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"For 50V at full scale, multiplier resistance should be\",int(Rs/1000),\" kilo ohm\"\n",
+ "print \"When instrument reads 0.8 FSD, applied voltage is\",int(V1),\" volt\"\n",
+ "print \"When instrument reads 0.5 FSD, applied voltage is\",int(V2),\" volt\"\n",
+ "print \"When instrument reads 0.2 FSD, applied voltage is\",int(V3),\" volt\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-7, Page Number: 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "For Circuit 1,\n",
+ "R1= 198.3 kilo ohm\n",
+ "R2= 998.3 kilo ohm\n",
+ "R3= 1.9983 mega ohm\n",
+ " \n",
+ "For Circuit 2,\n",
+ "R1= 198.3 kilo ohm\n",
+ "R2= 800 kilo ohm\n",
+ "R3= 1.0 mega ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable declaration\n",
+ "\n",
+ "Im=50*10**-6 #FSD current in A\n",
+ "Rm=1700 #Coil resistance in ohm\n",
+ "V1=10 #Required range in V\n",
+ "V2=50 #Required range in V\n",
+ "V3=100 #Required range in V\n",
+ "\n",
+ "#For Circuit 1\n",
+ "R11=V1/Im-Rm\n",
+ "R12=V2/Im-Rm\n",
+ "R13=V3/Im-Rm\n",
+ "\n",
+ "#For Circuit 2\n",
+ "R21=V1/Im-Rm\n",
+ "R22=V2/Im-R21-Rm\n",
+ "R23=V3/Im-R22-R21-Rm\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"For Circuit 1,\"\n",
+ "print \"R1=\",round(R11/1000,1),\"kilo ohm\"\n",
+ "print \"R2=\",round(R12/1000,1),\"kilo ohm\"\n",
+ "print \"R3=\",round(R13/10**6,4),\"mega ohm\"\n",
+ "\n",
+ "print \" \"\n",
+ "print \"For Circuit 2,\"\n",
+ "print \"R1=\",round(R21/1000,1),\"kilo ohm\"\n",
+ "print \"R2=\",int(R22/1000),\"kilo ohm\"\n",
+ "print \"R3=\",round(R23/10**6,4),\"mega ohm\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 3-8, Page Number: 53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 97,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Multiplier Resistance= 890.7 kilo ohm\n"
+ ]
+ },
+ {
+ "data": {
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+ "A+MgTQ0qgm8WAAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x79bf450>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "## Variable Declaration\n",
+ "\n",
+ "I=100*10**-6 #Full Scale Current in A\n",
+ "Rm=1*10**3 #Coil Resistance in ohm\n",
+ "Vrms=100 #FSD rms voltage in V \n",
+ "Vf=0.7 #Diode voltage\n",
+ "\n",
+ "\n",
+ "#At FSD, the average current flowing through PMMC is\n",
+ "Iavg=I\n",
+ "Im=round(Iavg/0.637,6)\n",
+ "\n",
+ "rectifier_voltage_drops=2*Vf\n",
+ "peak_voltage=1.414*Vrms\n",
+ "Rs=(peak_voltage-rectifier_voltage_drops)/Im-Rm\n",
+ "\n",
+ "#To plot rectified waveform used by the voltmeter at FSD\n",
+ "t=np.arange(0.01,1.0,0.01) #Time Axis\n",
+ "plt.plot(t,(peak_voltage-2*Vf)*fabs(sin(2*pi*t*2))) #Full wave rectified sine wave\n",
+ "plt.plot(t,(peak_voltage-2*Vf)*t/t,'--',label='Vm') #Peak Voltage Marker\n",
+ "plt.plot(t,(Vrms-0.707*2*Vf)*t/t,'--',label='Vrms') #RMS Voltage Marker\n",
+ "plt.plot(t,(peak_voltage-2*Vf)*0.637*t/t,'--',label='Vavg') #Average Voltage Marker\n",
+ "legend = plt.legend(loc='lower right')\n",
+ "xlabel('Time(second)')\n",
+ "ylabel('Input Voltage(V)')\n",
+ "title('Rectified waveform across PMMC at FSD')\n",
+ "\n",
+ "#Results\n",
+ "print \"Multiplier Resistance=\",round(Rs/1000,1), \"kilo ohm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 3-9, Page Number: 53\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "When input is 75 V(rms), meter reading is 0.75 FSD\n",
+ "When input is 50 V(rms), meter reading is 0.5 FSD\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration \n",
+ "#Data from Example 3-7\n",
+ "Rs=890*10**3 #in ohm \n",
+ "Rm=1*10**3 #in ohm\n",
+ "Vrms=100 #in V\n",
+ "Vf=0.7 #in V\n",
+ "I=100*10**-6 #in A\n",
+ "\n",
+ "#When input=75V (rms)\n",
+ "Vrms1=75\n",
+ "Im1=(1.414*Vrms1-2*Vf)/(Rs+Rm)\n",
+ "Iavg1=0.637*Im1\n",
+ "p1=Iavg1/I\n",
+ "\n",
+ "#When input=50V (rms)\n",
+ "\n",
+ "Vrms2=50\n",
+ "Im2=(1.414*Vrms2-2*Vf)/(Rs+Rm)\n",
+ "Iavg2=0.637*Im2\n",
+ "p2=Iavg2/I\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"When input is 75 V(rms), meter reading is\",round(p1,2),\" FSD\"\n",
+ "print \"When input is 50 V(rms), meter reading is\",round(p2,2),\" FSD\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-10, Page Number: 54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The sensitivity of the voltmeter described in example 3-8 is, 9 kilo ohm/V\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math \n",
+ "#Variable Declaration\n",
+ "#From Example 3-8\n",
+ "Im=157*10**-6 #Maximum Current(A)\n",
+ "Vrms=100 #Maximum rms voltage(V)\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "Irms=0.707*Im #Property of sinusoid \n",
+ "R=Vrms/Irms #Ohm's Law\n",
+ "sensitivity=R/Vrms\n",
+ "\n",
+ "print \"The sensitivity of the voltmeter described in example 3-8 is,\",int(sensitivity/1000),\"kilo ohm/V\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-11, Page Number: 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 96,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The value of Rsh is 778 ohm\n",
+ "The value of Rs is 139.5 kilo ohm\n"
+ ]
+ },
+ {
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+ "OKn4/5CFOt6sGQp8AAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7edddd0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import math\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Iav=50*10**-6 #FSD Current (A)\n",
+ "Rm=1700 #Coil resistance(ohm)\n",
+ "Imin=100*10**-6 #Minimum forward current (peak)in A\n",
+ "p=20.0/100.0 #20% FSD at 100 micro amps\n",
+ "Vrms=50\n",
+ "Vf=0.7\n",
+ "#Calculation\n",
+ "Im=Iav/(0.5*0.637) \n",
+ "\n",
+ "\n",
+ "#At 20% FSD, If must be 100micro amps, hence the current at 100% FSD is\n",
+ "If_peak=Imin/p\n",
+ "Ish_peak=If_peak-Im\n",
+ "Vm_peak=Im*Rm\n",
+ "Rsh=Vm_peak/Ish_peak\n",
+ "Rs=(1.414*Vrms-Vm_peak-Vf)/If_peak\n",
+ "\n",
+ "\n",
+ "#Plot of half wave rectified voltage appearing across PMMC instrument\n",
+ "t=np.arange(0.01,1.0,0.01) #Time Axis\n",
+ "N=0\n",
+ "x=zeros(99)\n",
+ "while(N<99):\n",
+ " if((N<=25)|(N>50)&(N<=75)):\n",
+ " x[N]=(If_peak-Im)*Rsh*sin(2*pi*2*N/100)\n",
+ " else:\n",
+ " x[N]=0\n",
+ " N=N+1\n",
+ " plt.plot(t,x)\n",
+ "plt.plot(t,(If_peak-Im)*Rsh*t/t,'--',label='Vmax')\n",
+ "plt.plot(t,0.5*(If_peak-Im)*Rsh*t/t,'--',label='Vrms')\n",
+ "plt.plot(t,0.318*(If_peak-Im)*Rsh*t/t,'--',label='Vavg')\n",
+ "plt.xlabel('Time(second)')\n",
+ "plt.ylabel('Voltage(V)')\n",
+ "plt.title('Half wave rectified waveform across PMMC at FSD')\n",
+ "legend = plt.legend(loc='lower right')\n",
+ "\n",
+ "#Results\n",
+ "print \"The value of Rsh is\",int(Rsh),\" ohm\"\n",
+ "print \"The value of Rs is\",round(Rs/1000,1),\" kilo ohm\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-12, Page Number: 58"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 111,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The required value of Rl is 28.2 kilo ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable Declaration\n",
+ "\n",
+ "Iav=1*10**-3 #in A\n",
+ "Rm=1700 #in ohm \n",
+ "Ns=500 #Secondary windings \n",
+ "Np=4 #Primary windings \n",
+ "Vf=0.7 #in V \n",
+ "Rs=20*10**3 #in ohm \n",
+ "Ip=250*10**-3 #in A\n",
+ "\n",
+ "#Calculation\n",
+ "Im=Iav/0.637 #Property of sine half wave\n",
+ "Em=Im*(Rs+Rm)+2*Vf \n",
+ "Es=0.707*Em\n",
+ "rms_meter_current=1.11*Iav\n",
+ "\n",
+ "#Trasnformer rms secondary current is,\n",
+ "Is=Ip*Np/Ns\n",
+ "\n",
+ "Il=Is-rms_meter_current\n",
+ "Rl=Es/Il\n",
+ "\n",
+ "print \"The required value of Rl is\",round(Rl/1000,1),\" kilo ohm\" \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-13, Page Number: 59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 129,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "At FSD,\n",
+ "Measured current= 99.0 micro ampere to 101.0 micro ampere\n",
+ "Error=± 1 % of measured current\n",
+ " \n",
+ "At 0.5 FSD,\n",
+ "Measured current= 49.0 micro ampere to 51.0 micro ampere\n",
+ "Error= ± 2 % of measured current\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#Variable Delcaration\n",
+ "\n",
+ "current_fsd=100*10**-6\n",
+ "accuracy=1.0/100.0\n",
+ "\n",
+ "#Calculation\n",
+ "error_fsd=accuracy*current_fsd\n",
+ "#At FSD\n",
+ "indicated_current_fsd=current_fsd\n",
+ "measured_current_fsd_max=indicated_current_fsd+error_fsd\n",
+ "measured_current_fsd_min=indicated_current_fsd-error_fsd\n",
+ "\n",
+ "\n",
+ "#At 0.5 FSD\n",
+ "\n",
+ "indicated_current=0.5*current_fsd\n",
+ "measured_current_max=indicated_current+error_fsd\n",
+ "measured_current_min=indicated_current-error_fsd\n",
+ "\n",
+ "error=error_fsd/indicated_current\n",
+ "\n",
+ "#Results \n",
+ "\n",
+ "print \"At FSD,\"\n",
+ "print \"Measured current=\",measured_current_fsd_min*10**6,\" micro ampere to\",measured_current_fsd_max*10**6,\" micro ampere\"\n",
+ "print \"Error=±\",int(accuracy*100),\"% of measured current\"\n",
+ "\n",
+ "print \" \"\n",
+ "print \"At 0.5 FSD,\"\n",
+ "print \"Measured current=\",measured_current_min*10**6,\" micro ampere to\",measured_current_max*10**6,\" micro ampere\"\n",
+ "print \"Error= ±\",int(error*100),\"% of measured current\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-14, Page Number: 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "When Rx=0, the meter indicates 100 micro ampere(FSD)\n",
+ " \n",
+ "At 0.5 FSD, Rx= 15 kilo ohm\n",
+ "At 0.25 FSD, Rx= 45 kilo ohm\n",
+ "At 0.75 FSD, Rx= 5.0 kilo ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#Variable Declaration\n",
+ "Eb=1.5 #Battery Voltage(V)\n",
+ "R1=15.0*10**3 #Standard resistance+meter resistance\n",
+ "\n",
+ "Im=Eb/R1 #Ohm's Law\n",
+ "\n",
+ "#At 0.5 FSD\n",
+ "Im1=0.5*Im #Current at 0.5 FSD\n",
+ "Rx1=Eb/Im1-R1 #Resistance measured at 0.5 FSD\n",
+ "\n",
+ "#At 0.25 FSD\n",
+ "Im2=Im/4\n",
+ "Rx2=Eb/Im2-Rx1 #Resistance measured at 0.25 FSD \n",
+ "\n",
+ "#At 0.75 FSD \n",
+ "Im3=0.75*Im\n",
+ "Rx3=Eb/Im3-Rx1 #Resistance measured at 0.25 FSD \n",
+ "\n",
+ "#Results\n",
+ "print \"When Rx=0, the meter indicates\",int(Im*10**6),\"micro ampere(FSD)\"\n",
+ "print \" \"\n",
+ "print \"At 0.5 FSD, Rx=\",int(Rx1*10**-3),\" kilo ohm\"\n",
+ "print \"At 0.25 FSD, Rx=\",int(Rx2*10**-3),\" kilo ohm\"\n",
+ "print \"At 0.75 FSD, Rx=\",round(Rx3*10**-3),\" kilo ohm\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-15, Page Number: 63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Ohmmeter scale reading at 0.5 FSD is, 15 kilo ohm\n",
+ "With Rx=0 and Eb=1.3V, R2 should be 68.18 ohm\n",
+ "At 0.5 FSD, with Eb=1.3V, the ohmeter scale reading is, 15 kilo ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#Variable Declaration\n",
+ "Eb1=1.5 #Battery Voltage(V)\n",
+ "R1=15*10**3 #Series resistance as shown in figure(ohm)\n",
+ "Rm=50 #Coil resistance (ohm)\n",
+ "R2=50 #Shunt resistance(ohm)\n",
+ "I_fsd=50*10**-6 #FSD Current(A) \n",
+ "Eb2=1.3\n",
+ "\n",
+ "\n",
+ "#At 0.5 FSD, with Eb=1.5V\n",
+ "Im1=0.5*I_fsd\n",
+ "Vm1=Im1*Rm\n",
+ "I21=Vm1/R2 #Ohm's Law\n",
+ "Ib1=I21+Im1 #KCL\n",
+ "Rx1=Eb1/Ib1-R1 #Unknown resistance value is found \n",
+ "\n",
+ "#With Rx=0,Eb=1.3V\n",
+ "\n",
+ "Ib2=Eb2/R1 #Total Current \n",
+ "I22=Ib2-I_fsd #Shunt Current using KCL\n",
+ "Vm2=I_fsd*Rm #Voltage across meter\n",
+ "R22=Vm2/I22 #Shunt Resistance value\n",
+ "\n",
+ "#At 0.5FSD, Eb=1.3V\n",
+ "Im3=0.5*I_fsd #Meter Current\n",
+ "Vm3=Im3*Rm #Voltage across meter using Ohm's Law\n",
+ "I23=Vm3/R22 #Shunt Current using Ohm's Law \n",
+ "Ib3=I23+Im3 #Total current using KCL \n",
+ "Rx2=Eb2/Ib3-R1 #Resitance reading on Ohm scale\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"Ohmmeter scale reading at 0.5 FSD is,\",int(Rx1/1000),\"kilo ohm\"\n",
+ "print \"With Rx=0 and Eb=1.3V, R2 should be\",round(R22,2),\"ohm\"\n",
+ "print \"At 0.5 FSD, with Eb=1.3V, the ohmeter scale reading is,\",int(Rx2/1000),\"kilo ohm\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3-16, Page Number: 65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "When Rx=0,\n",
+ "Battery current= 62.516 mA\n",
+ "Meter current= 37.45 micro ampere\n",
+ "Full Scale= 0 ohm\n",
+ " \n",
+ "When Rx=24,\n",
+ "Battery Current= 31.254 mA\n",
+ "Meter Current= 18.72 micro ampere\n",
+ "As meter current is 0.5 times of full scale.Thus, when Rx=24 ohm it indicates half scale reading\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#Variable Declaration\n",
+ "#From Circuit Diagram\n",
+ "R1=14 #in ohm\n",
+ "R2=10 #in ohm \n",
+ "R3=9.99*10**3 #in ohm \n",
+ "R4=2.875*10**3 #in ohm\n",
+ "R5=3.82*10**3 #in ohm \n",
+ "Eb=1.5 #Battery current\n",
+ "#Calculation\n",
+ "\n",
+ "#When Rx=0, battery current is\n",
+ "R6=R3+R4+R5 #Series equivalent\n",
+ "R7=R2*R6/(R2+R6) #Parallel equivalent \n",
+ "Ib1=Eb/(R1+R7) \n",
+ "Im1=Ib1*R2/(R2+R6) #Using Current Dividor Rule \n",
+ "\n",
+ "#When Rx=24 ohm,\n",
+ "R8=24 \n",
+ "Ib2=Eb1/(R8+R1+R7) #From figure\n",
+ "Im2=Ib2*R2/(R2+R6) #Using Current Dividor Rule\n",
+ "n=round(Ib2/Ib1,3)\n",
+ "#Results\n",
+ "\n",
+ "print \"When Rx=0,\"\n",
+ "print \"Battery current=\",round(Ib1*1000,3),\" mA\"\n",
+ "print \"Meter current=\",round(Im1*10**6,2),\" micro ampere\"\n",
+ "print \"Full Scale= 0 ohm\"\n",
+ "\n",
+ "print \" \"\n",
+ "print \"When Rx=24,\"\n",
+ "print \"Battery Current=\",round(Ib2*10**3,3),\"mA\"\n",
+ "print \"Meter Current=\",round(Im2*10**6,2),\"micro ampere\"\n",
+ "print \"As meter current is\",n,\"times of full scale.Thus, when Rx=24 ohm it indicates half scale reading\" \n",
+ "\n"
+ ]
+ }
+ ],
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generated by cgit (git 2.34.1) at 2024-12-20 05:11:00 +0000