{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 4 - Potentiometers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1 - pg 256" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Unknown resistor (ohm) = 0.08275\n" ] } ], "source": [ "#pg 256\n", "#Example 4.1: Unknown resistor\n", "#calculate the Unknown resistor\n", "#given data :\n", "Vd=0.83942;# volt-drop in V\n", "emf=23*10**-6;# in V\n", "Vds=1.01575;# volt-drop in V\n", "Rs=0.10014;# in ohm\n", "#calculations\n", "Vdt=Vd-emf;# in V\n", "I=Vds/Rs;\n", "R=Vdt/I;\n", "#results\n", "print \"Unknown resistor (ohm) = \",round(R,5)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2 - pg 257" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(a). emf of the cell,(V) = 1.42562\n", "(b). % error (high),(%) = 1.98\n", "(c). % error (high),(%) = 1.59\n" ] } ], "source": [ "#pg 257\n", "#Example 4.2: emf and % error \n", "#calculate the emf and % error \n", "#given data :\n", "l=50;# in cm\n", "l1=70;# in cm\n", "l2=65;# in cm\n", "l3=43.5;# in cm\n", "I=0.45;# in A\n", "V=1.0183;# in V\n", "V1=1.35;# in V\n", "R=2;# in ohm\n", "#calculations\n", "Vpl=V/l;# in V/cm\n", "emf=Vpl*l1;\n", "Vr=Vpl*l2;\n", "P_error1=((V1-Vr)/Vr)*100;\n", "Ir=(Vpl*l3)/R;# in A\n", "P_error2=((I-Ir)/Ir)*100;\n", "#results\n", "print \"(a). emf of the cell,(V) = \",emf\n", "print \"(b). % error (high),(%) = \",round(P_error1,2)\n", "print \"(c). % error (high),(%) = \",round(P_error2,2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3 - pg 258" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "part a \n", "current is (A)= 0.02\n", "resistance is (ohm)= 100.0\n", "part b\n", "current is (mA)= 7.078\n", "resistance is (k-ohm)= 2035.32\n", "resistance is calculated wrong in the textbook\n" ] } ], "source": [ "#pg 258\n", "#Example 4.3.a: current and resistance\n", "#calculate the current and resistance\n", "#given\n", "import numpy\n", "from numpy import linalg\n", "e1=1.0191;#V\n", "r1=100.;#ohms\n", "l=2;#m\n", "e2=4;#V\n", "#calculations and results\n", "I=l/r1;#A\n", "rh=(e2/I)-r1;#\n", "print 'part a '\n", "print \"current is (A)=\",I\n", "print \"resistance is (ohm)=\",rh\n", "e1=4;#V\n", "e2=1.0191;#V\n", "R1=100;#OHM\n", "R2=49.045;#OHMS\n", "r3=R1-R2;#ohms\n", "rg=50;#ohms\n", "r4=200;#ohms\n", "A=numpy.matrix([[r4, -r3],[-r3, (r4+rg+r3)]]);#\n", "B=numpy.matrix([[e1],[e2]]);#\n", "X=numpy.dot(numpy.linalg.inv(A),B)\n", "I2=X[1,0]*10**3;#\n", "I1=((e1+(r3*10**-5))/r4);#mA\n", "rp=((e2+(r3*I1)-(r4+rg+r3)*10**-5)/10**-5);#\n", "#results\n", "print 'part b'\n", "print \"current is (mA)=\",round(I2,3)\n", "print \"resistance is (k-ohm)=\",round(rp*10**-2,2)\n", "print 'resistance is calculated wrong in the textbook'\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4 - pg 259" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "internal resistance,Ri(ohm) = 176.689\n" ] } ], "source": [ "#pg 259\n", "#Example 4.4: Resistance\n", "#calculate the internal resistance\n", "#given data :\n", "emf=1.01892;# in V\n", "R=1;# in M-ohm\n", "V=1.01874;# in V\n", "#calculations\n", "Ic=V/R;\n", "Vd=emf-V;\n", "Ri=Vd/(Ic*10**-6);\n", "#results\n", "print \"internal resistance,Ri(ohm) = \",round(Ri,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5 - pg 259" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Internal resistance,Ri(ohm) = 3.636\n" ] } ], "source": [ "#pg 259\n", "#Example 4.5: Resistance\n", "#calculate the resistance\n", "#given data :\n", "l=65;# in cm\n", "V=0.1;# in V\n", "V1=5.5;# in V\n", "R=20;# in ohm\n", "#calculations\n", "E=V*l;\n", "I=V1/R;\n", "Ri=(E-V1)/I;\n", "#results\n", "print \"Internal resistance,Ri(ohm) = \",round(Ri,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6 - pg 259" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resistance is (k-ohm)= 50.0\n" ] } ], "source": [ "#pg 259\n", "#Example 4.6: Resistance\n", "#calculate the resistance\n", "#given\n", "vr=5.;#V\n", "r=10.;#k-ohm\n", "#calculations\n", "x=vr*r*10**3;#\n", "R=x;#\n", "#results\n", "print \"resistance is (k-ohm)=\",R*10**-3\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 7 - pg 260" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The length of slide wire (cm) = 200.0\n" ] } ], "source": [ "#pg 260\n", "#Example 4.7: Length\n", "#calculate the length of the slide wire\n", "#given data :\n", "l=40.;# in cm\n", "r=0.5;# ion ohm\n", "V=1.2;# in V\n", "V1=6;# in V\n", "#calculations\n", "R=r*l/1;# in ohm\n", "I=V/R;\n", "x=V1/(r*I);\n", "#results\n", "print \"The length of slide wire (cm) = \",x\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 8 - pg 260" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resistance R is (ohm)= 20.0\n", "resistance R1 is (ohm)= 2.0\n", "resistance R2 is (ohm)= 4.0\n", "resistance per cm of slide wire is (ohm/cm)= 0.02\n" ] } ], "source": [ "#pg 260\n", "#Example 4.8: design\n", "#calculate the resistance in all cases\n", "#given\n", "vab=1.;#V\n", "i=50.;#mA\n", "n=10.;#\n", "l=100.;#cm\n", "#calculations\n", "vr=2-vab;#V\n", "R=vr/(i*10**-3);#ohm\n", "R1=(vr/10)/(i*10**-3);#ohm\n", "tr1=n*R1;#ohm\n", "r2=2*R1;#\n", "x=R1/l;#\n", "#results\n", "print \"resistance R is (ohm)=\",R\n", "print \"resistance R1 is (ohm)=\",R1\n", "print \"resistance R2 is (ohm)=\",r2\n", "print \"resistance per cm of slide wire is (ohm/cm)=\",x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 9 - pg 261" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resistance is (ohm) = 39.5\n", "resolution of the instrument is (micro-V) = 20.0\n", "error is (micro-V) = 2.5\n" ] } ], "source": [ "#pg 261\n", "#Example 4.9.a:resistance\n", "#calculate the resistance, resolution and error\n", "#given\n", "st=15.;#steps\n", "r=5.;#ohm\n", "rsw=5.5;#ohm\n", "vr=1.61;#V\n", "e2=1.61;#V\n", "e1=2.40;#V\n", "trn=11.;#turns\n", "dv=100.;#divisions\n", "ig=0.05;#micro-A\n", "vlt=1.1;#V\n", "ir=50.;#ohm\n", "#calculations\n", "tr=(st*r)+rsw;#ohm\n", "i=vr/tr;#A\n", "rh=(e1-e2)/i;#ohm \n", "slwr=rsw/trn;#ohm\n", "vd=slwr*i;#V\n", "vedv=(1/dv)*vd;#\n", "rs=vedv/5;#\n", "em=((ig*ir));#\n", "#results\n", "print \"resistance is (ohm) = \",rh\n", "print \"resolution of the instrument is (micro-V) = \",rs*10**6\n", "print \"error is (micro-V) = \",em\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10 - pg 262" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "power dissipated in the resistor is (mW)= 0.4176\n", "power dissipated in the coil is (mW)= 0.264\n", "power dissipated in the capacitor is (mW)= 0.036\n", "energy stored in the coil is (micro-J)= 0.61\n", "energy stored in capacitor is (micro-J)= 0.42\n" ] } ], "source": [ "#pg 262\n", "#Example 4.10:power dissipated\n", "#calculate the power dissipated and energy stored\n", "#given\n", "import math,cmath\n", "r1=0.6-1j*0.24;#V\n", "r2=0.6+1j*0.4;#V\n", "r3=-0.1-1j*0.4;#V\n", "f=50;#Hx\n", "ir=1000;#ohm\n", "#calculations\n", "i1=r1/ir;#A\n", "pdr=(r1.real*i1.real)+(r1.imag*i1.imag);#W\n", "pdC=(r1.real*i1.real)+(r2.imag*i1.imag);#W\n", "pdc=(r3.real*i1.real)-(r2.imag*i1.imag);#W\n", "imp=(r2/r1)*10**3;#ohm\n", "rc=imp.imag;#ohm\n", "indu=rc/(2*math.pi*f);#H\n", "ersl=(1./2)*(i1.imag**2+i1.real**2)*indu;#joules\n", "admc=(r1*10**-3)/r3;#ohm**-1\n", "C=admc.imag/(2*math.pi*f);#\n", "ersc=(1./2)*(r3.imag**2+r3.real**2)*C;#\n", "#results\n", "print \"power dissipated in the resistor is (mW)=\",pdr*10**3\n", "print \"power dissipated in the coil is (mW)=\",pdC*10**3\n", "print \"power dissipated in the capacitor is (mW)=\",pdc*10**3\n", "print \"energy stored in the coil is (micro-J)=\",round(ersl*10**6,2)\n", "print \"energy stored in capacitor is (micro-J)=\",round(ersc*10**6,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11 - pg 263" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "measuring range of the potentiometer is (V)= 1.9\n", "resolution is (mV)= 0.5\n", "current through the dial is (mA)= 10.0\n", "setting of the rheostat is (ohm)= 410.0\n" ] } ], "source": [ "#pg 263\n", "#Example 4.11:measuring range,resulution,working current,setting of the rheostat\n", "#calculate the measuring range,resulution,working current,setting of the rheostat\n", "#given\n", "sd=18.;#steps\n", "v1=0.1;#V\n", "dv=100;#divisions\n", "dr=10;#ohm\n", "wbc=6;#V\n", "#calculations\n", "mr=(sd*v1)+v1;#V\n", "rs=(v1/dv)*(1./2);#mV\n", "cdd=v1/dr;#A\n", "rsv=wbc-mr;#V\n", "sh=rsv/cdd;#ohm\n", "#results\n", "print \"measuring range of the potentiometer is (V)=\",mr\n", "print \"resolution is (mV)=\",rs*10**3\n", "print \"current through the dial is (mA)=\",cdd*10**3\n", "print \"setting of the rheostat is (ohm)=\",sh\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 12 - pg 263" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "true value of drop across the resistance is (V)= 0.6529\n", "percentage error is (%)= 0.06\n" ] } ], "source": [ "#pg 263\n", "#Example 4.12:voltage and percentage error\n", "#calculate the voltage and percentage error\n", "#given\n", "st=15;#steps\n", "r1=10;#ohm\n", "v1=0.1;#V\n", "r2=10;#ohm\n", "r3=9.9;#ohm\n", "v2=0.0185;#V\n", "v3=1.0185;#V\n", "n=6;#\n", "vg=0.6525;#\n", "#calculations\n", "acr=(r1*r3)+((r2*v2)/v1);#ohm\n", "I=v3/acr;#\n", "acr1=(n*r3)+(r2*0.0525)/v1;#ohm\n", "tvr=I*acr1;#V\n", "er=((tvr-vg)/tvr)*100;#\n", "#results\n", "print \"true value of drop across the resistance is (V)=\",round(tvr,4)\n", "print \"percentage error is (%)=\",round(er,2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 13 - pg 264" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "reactance is (ohm)= 1.28\n", "inductance of the coil is (mH)= 30.0\n", "The answer is a bit different due to rounding off error in textbook\n" ] } ], "source": [ "#pg 264\n", "#Example 4.13:resistance and reactance\n", "#calculate the resistance and reactance\n", "#given\n", "import math,cmath\n", "from math import sqrt,atan,sin\n", "r1=2.;#ohm\n", "r2=9.;#\n", "vm=85.;#V\n", "va=40.;#degree\n", "vm1=90.;#V\n", "va1=45.;#degree\n", "f=50.;#Hz\n", "#calculations\n", "imp=r1+1j*r2;#ohm\n", "mg=sqrt(r1**2+r2**2);#\n", "th=atan(r2/r1) *57.3;#\n", "ccm=vm/mg;#A\n", "cca=va-th;#degree\n", "impm=vm1/ccm;#ohm\n", "impa=va1-cca;#degree\n", "reac=impm*sin(impa/57.3);#ohm\n", "rc=sqrt(impm**2-reac**2);#ohm\n", "ind=reac/(2*math.pi*f);#\n", "#results\n", "print \"reactance is (ohm)=\",round(rc,2)\n", "print \"inductance of the coil is (mH)=\",math.floor(ind*10**3)\n", "print 'The answer is a bit different due to rounding off error in textbook'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 14 - pg 265" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "limit of error in the reading is 48.6 micro-V\n", "deflection of the galvanometer is (mm)= 8.1\n" ] } ], "source": [ "#pg 265\n", "#Example 4.14:limit of error,deflection\n", "#calculate the limit of error and deflection of galvanometer\n", "#given\n", "x=17.5;#mm/micro-A\n", "r1=850.;#ohm\n", "v1=2.;#V\n", "r2=80.;#\n", "v3=1.43;#V\n", "v2=0.1;#V\n", "l=50.;#cm\n", "l1=2.;#mm\n", "fr1=22.784;#\n", "#calculations\n", "lr=r1*(1./x);#micro V\n", "i1=v1/r2;#A\n", "r3=v2/i1;#ohm\n", "r4=v3/i1;#ohm\n", "r5=((l1/10.)/l)*r3;#ohm\n", "fr=r4+r5;#ohm\n", "R=(fr*fr1)/r2;#ohm\n", "e=i1*fr;#V\n", "ig=(e-v3)/(r1+R);#A\n", "dg=ig*x*10**6;#mm\n", "#results\n", "print \"limit of error in the reading is \",round(lr,1),\" micro-V\"\n", "print \"deflection of the galvanometer is (mm)=\",round(dg,1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 15 - pg 266" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Current in one direction,I1(mA) = 10.0\n", "Current in another direction,I2(mA) = 10.34\n" ] } ], "source": [ "#pg 266\n", "#Example 4.15: Current \n", "#calculate the Current \n", "#given data :\n", "V1=4.2;# in V\n", "V2=1.43;# in V\n", "r1=21.0;# in ohm\n", "r2=1.;# in ohm\n", "r3=15.;# in ohm\n", "#calculations\n", "I=V1/r1;# in A\n", "R=V2/I;# in ohm\n", "R1=R+r2;\n", "R2=R-r2;\n", "R3=round(R1*(r1-R1)/r1);\n", "R4=R2*(r1-R2)/r1;\n", "e1=R1*I;\n", "e2=R2*I;\n", "I1=(e1-V2)*10**3/(R3+r3);\n", "I2=(V2-e2)*10**3/(R4+r3);\n", "#results\n", "print \"Current in one direction,I1(mA) = \",I1\n", "print \"Current in another direction,I2(mA) = \",round(I2,2)\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 }