{ "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": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Multiplier Resistance= 890.7 kilo ohm\n" ] }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEZCAYAAACNebLAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXm4XEW1t98fYZ4CCZCEQNJhjIwqCKICB0QvAoIiijgB\n", "jp8TzgpOxKuiqNfh6lWvKJMIiKAMV0BwOIiCIjLPBOiMJEASSBgTyPr+qOpkp9PdZ3f3nrve5+nn\n", "9N69u/bqdWrXqlpVtZbMjEAgEAgEmlkjbwECgUAgUEyCgQgEAoFAS4KBCAQCgUBLgoEIBAKBQEuC\n", 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math\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\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", "\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", "x=np.zeros(99)\n", "N=0\n", "while(N<99):\n", " x[N]=(peak_voltage-2*Vf)*math.fabs(math.sin(2*math.pi*N*2/100))\n", " N=N+1\n", "\n", "plt.plot(t,x) #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", "plt.xlabel('Time(second)')\n", "plt.ylabel('Input Voltage(V)')\n", "plt.title('Rectified waveform across PMMC at FSD')\n", "\n", "#Results\n", "print \"Multiplier Resistance=\",round(Rs/1000,1), \"kilo ohm\"\n", "\n", "\n" ] }, { "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": 2, "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" ] }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEZCAYAAACEkhK6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXnYXEWV/z/fBBBIwIAsIUBIIAECgizKLgRRiTCCOigi\n", "4iA6ooL6Q50BnRkJigoj4qgoIoPKjoqg0WEXgoBhCQQIECAJBEIW1pAECJKQ8/ujqpObTne/t/vt\n", "2/f27fN5nn7eu1TVPbfeqnuqTi1HZobjOI7j9MWAvAVwHMdxugNXGI7jOE4qXGE4juM4qXCF4TiO\n", "46TCFYbjOI6TClcYjuM4TipcYbQBScdKui1xvq+k6ZIWSzosT9nyRtI1ko5JnJ8u6XlJcyVtGfNI\n", "LaQ7QtJySYUsw14GnDJSyMrWaSTNknRQ1bVVlECTfBv4iZmtZ2YT+i9hdyBpvKSLk9fM7BAzuzje\n", 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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=np.zeros(99)\n", "while(N<99):\n", " if((N<=25)|(N>50)&(N<=75)):\n", " x[N]=(If_peak-Im)*Rsh*math.sin(2*math.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\"" ] }, { "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" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }