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diff --git a/Physics_for_BSc(Paper-3)/Chapter9.ipynb b/Physics_for_BSc(Paper-3)/Chapter9.ipynb new file mode 100755 index 00000000..67ff399f --- /dev/null +++ b/Physics_for_BSc(Paper-3)/Chapter9.ipynb @@ -0,0 +1,693 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:aec700ae8e541452237ee9c0f10eb2b8642d7039520473250339382162750967"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "9: Varying and alternating currents"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.1, Page number 242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=0.1; #inductance(H)\n",
+ "R=10; #resistance(ohm)\n",
+ "t1=0; #time(sec)\n",
+ "t2=0.002; #time(sec)\n",
+ "t3=0.04; #time(sec)\n",
+ "E=5; #voltage(V)\n",
+ "\n",
+ "#Calculation\n",
+ "tow=L/R; #time(sec)\n",
+ "a=E/R;\n",
+ "i1=a*(1-math.exp(-t1/tow)); #current for t=0 sec(A)\n",
+ "i2=a*(1-math.exp(-t2/tow)); #current for t=0.002 sec(A)\n",
+ "i3=a*(1-math.exp(-t3/tow)); #current for t=0.04 sec(A)\n",
+ "i4=a*(1-math.exp(-tow/tow)); #current for t=tow sec(A)\n",
+ "\n",
+ "#Result\n",
+ "print \"current for t=0 sec is\",i1,\"A\"\n",
+ "print \"current for t=0.002 sec is\",round(i2,2),\"A\"\n",
+ "print \"current for t=0.04 sec is\",round(i3,2),\"A\"\n",
+ "print \"current for t=tow sec is\",round(i4,3),\"A\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current for t=0 sec is 0.0 A\n",
+ "current for t=0.002 sec is 0.09 A\n",
+ "current for t=0.04 sec is 0.49 A\n",
+ "current for t=tow sec is 0.316 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.2, Page number 243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=0.5; #inductance(H)\n",
+ "R=5; #resistance(ohm)\n",
+ "E=2; #voltage(V)\n",
+ "t=0.2; #time(sec)\n",
+ "\n",
+ "#Calculation\n",
+ "tow=L/R; #time(sec)\n",
+ "a=E/R;\n",
+ "i=a*(1-math.exp(-t/tow)); #current(A)\n",
+ "dibydt=(E-(R*i))/L; #rate of growth of current(A/s)\n",
+ "E=(1/2)*L*(i**2); #energy stored by inductor(J)\n",
+ "\n",
+ "#Result\n",
+ "print \"rate of growth of current is\",round(dibydt,2),\"A/s\"\n",
+ "print \"energy stored by inductor is\",round(E,2),\"J\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rate of growth of current is 0.54 A/s\n",
+ "energy stored by inductor is 0.03 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.3, Page number 244"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=10; #inductance(H)\n",
+ "R=10; #resistance(ohm)\n",
+ "E=10; #voltage(V)\n",
+ "t1=0.3; #time(sec)\n",
+ "t2=0.5; #time(sec)\n",
+ "t3=1; #time(sec)\n",
+ "\n",
+ "#Calculation\n",
+ "tow=L/R; #time(sec)\n",
+ "i0=E/R;\n",
+ "i1=i0*math.exp(-t1/tow); #current for t=0.3 sec(A)\n",
+ "i2=i0*math.exp(-t2/tow); #current for t=0.5 sec(A)\n",
+ "i3=i0*math.exp(-t3/tow); #current for t=1 sec(A)\n",
+ "\n",
+ "#Result\n",
+ "print \"current for t=0.3 sec is\",round(i1,2),\"A\"\n",
+ "print \"current for t=0.5 sec is\",round(i2,2),\"A\"\n",
+ "print \"current for t=1 sec is\",round(i3,2),\"A\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current for t=0.3 sec is 0.74 A\n",
+ "current for t=0.5 sec is 0.61 A\n",
+ "current for t=1 sec is 0.37 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.4, Page number 250"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "E=5; #voltage(V)\n",
+ "C=2*10**-6; #capacitor(F)\n",
+ "R=1*10**6; #resistance(ohm)\n",
+ "t=1; #time(sec)\n",
+ "v=40/100; #decay value(%)\n",
+ "\n",
+ "#Calculation\n",
+ "q=E*C*(1-math.exp(-t/(R*C))); #charge on plates(C)\n",
+ "Vc=q/C; #voltage drop across capacitor(V)\n",
+ "i0=E/R;\n",
+ "i=i0*math.exp(-t/(R*C)); #current in circuit(A)\n",
+ "V=i*R; #voltage drop across resistor(V)\n",
+ "E=(1/2)*C*(Vc**2); #energy stored by capacitor(J)\n",
+ "tow=R*C; #time constant(sec)\n",
+ "t=2*math.log(1/v); #time taken(sec)\n",
+ "\n",
+ "#Result\n",
+ "print \"voltage drop across capacitor is\",round(Vc,2),\"V\"\n",
+ "print \"current in circuit is\",int(i*10**6),\"micro A\"\n",
+ "print \"voltage drop across resistor is\",int(V),\"V\"\n",
+ "print \"energy stored by capacitor is\",round(E*10**6,1),\"*10**-6 J\"\n",
+ "print \"time constant is\",tow,\"sec\"\n",
+ "print \"time taken is\",round(t,4),\"sec\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage drop across capacitor is 1.97 V\n",
+ "current in circuit is 3 micro A\n",
+ "voltage drop across resistor is 3 V\n",
+ "energy stored by capacitor is 3.9 *10**-6 J\n",
+ "time constant is 2.0 sec\n",
+ "time taken is 1.8326 sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.5, Page number 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L=1*10**-3; #inductance(H)\n",
+ "C=0.1*10**-6; #capacitor(F)\n",
+ "R=1; #resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "a=1/(L*C);\n",
+ "b=(R**2)/(4*(L**2)); \n",
+ "omega=math.sqrt(a-b); #angular frequency(per sec)\n",
+ "Q=omega*L/R; #Q-factor\n",
+ "\n",
+ "#Result\n",
+ "print \"angular frequency is\",round(omega),\"per sec\"\n",
+ "print \"answer varies due to rounding off errors\"\n",
+ "print \"Q-factor is\",round(Q)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "angular frequency is 99999.0 per sec\n",
+ "answer varies due to rounding off errors\n",
+ "Q-factor is 100.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.6, Page number 280"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#v=7sin(314+pi/6)\n",
+ "v=7;\n",
+ "R=100; #resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "Im=v/R; #maximum current(A)\n",
+ "Irms=Im/math.sqrt(2); #rms value of current(A)\n",
+ "Vrms=v/math.sqrt(2);\n",
+ "P=Vrms*Irms; #average power(W)\n",
+ "\n",
+ "#Result\n",
+ "print \"maximum current is\",Im,\"A\"\n",
+ "print \"rms value of current is\",round(Irms,2),\"A\"\n",
+ "print \"average power is\",round(P,3),\"W\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum current is 0.07 A\n",
+ "rms value of current is 0.05 A\n",
+ "average power is 0.245 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.7, Page number 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#V=7sin(314t+pi/6)\n",
+ "v=7;\n",
+ "omega=314; \n",
+ "L=0.05; #inductance(H)\n",
+ "\n",
+ "#Calculation\n",
+ "XL=omega*L;\n",
+ "betaL=1/XL; #susceptance(per ohm)\n",
+ "i=v*betaL; #current through inductor\n",
+ "Im=i;\n",
+ "Irms=Im/math.sqrt(2); #rms current(A)\n",
+ "P=0; #power loss\n",
+ "\n",
+ "#Result\n",
+ "print \"susceptance is\",round(betaL,4),\"per ohm\"\n",
+ "print \"current through inductor is\",round(i,2),\"sin(314t-math.pi/3)\"\n",
+ "print \"rms current is\",round(Irms,2),\"A\"\n",
+ "print \"power loss is\",P"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "susceptance is 0.0637 per ohm\n",
+ "current through inductor is 0.45 sin(314t-math.pi/3)\n",
+ "rms current is 0.32 A\n",
+ "power loss is 0\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.8, Page number 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#V=7sin(314t+pi/6)\n",
+ "v=7;\n",
+ "omega=314; \n",
+ "C=0.05*10**-6; #capacitance(F)\n",
+ "\n",
+ "#Calculation\n",
+ "XC=1/(omega*C); #value of XC \n",
+ "i=v/XC; #current through capacitor\n",
+ "Im=i;\n",
+ "Irms=Im/math.sqrt(2); #rms current(A)\n",
+ "P=0; #power loss\n",
+ "\n",
+ "#Result\n",
+ "print \"value of XC is\",round(XC/10**3,1),\"K ohm\"\n",
+ "print \"current through capacitor is\",i*10**3,\"*10**-3 sin(314t+2*math.pi/3)\"\n",
+ "print \"rms current is\",int(Irms*10**6),\"micro A\"\n",
+ "print \"power loss is\",P"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of XC is 63.7 K ohm\n",
+ "current through capacitor is 0.1099 *10**-3 sin(314t+2*math.pi/3)\n",
+ "rms current is 77 micro A\n",
+ "power loss is 0\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.9, Page number 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "V1=110; #voltage(V)\n",
+ "P=40; #power(W)\n",
+ "V2=230; #voltage(V)\n",
+ "\n",
+ "#Calculation\n",
+ "RB=V1**2/P; #resistance of bulb(ohm)\n",
+ "i=V1/RB; #electric current through bulb(A)\n",
+ "Z=V2/i; #series resistance(ohm)\n",
+ "R=Z-RB; #pure resistance(ohm)\n",
+ "XL=math.sqrt((Z**2)-(RB**2)); \n",
+ "L=XL/314; #inductance(H)\n",
+ "\n",
+ "#Result\n",
+ "print \"pure resistance is\",R,\"ohm\"\n",
+ "print \"inductance is\",round(L,3),\"H\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pure resistance is 330.0 ohm\n",
+ "inductance is 1.769 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.10, Page number 311"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "C=10**-6; #capacitance(F)\n",
+ "L=10*10**-3; #inductance(H)\n",
+ "R=1*10**3; #resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "fr=1/(2*math.pi*math.sqrt(L*C)); #resonant frequency(Hz)\n",
+ "Z=L/(C*R); #impedence(ohm)\n",
+ "\n",
+ "#Result\n",
+ "print \"resonant frequency is\",round(fr/10**3,3),\"KHz\"\n",
+ "print \"impedence is\",Z,\"ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "resonant frequency is 1.592 KHz\n",
+ "impedence is 10.0 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.11, Page number 312"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "C=5*10**-6; #capacitance(F)\n",
+ "R=10; #resistance(ohm)\n",
+ "new=50; #frequency(Hz)\n",
+ "\n",
+ "#Calculation\n",
+ "omega=2*math.pi*new;\n",
+ "L=1/(C*(omega**2)); #self inductance(H)\n",
+ "\n",
+ "#Result\n",
+ "print \"self inductance is\",round(L,3),\"H\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "self inductance is 2.026 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.12, Page number 312"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "C=0.1*10**-6; #capacitance(F)\n",
+ "L=1*10**-3; #inductance(H)\n",
+ "R=10; #resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "omega0=1/math.sqrt(L*C); #resonant frequency(rad/sec)\n",
+ "d=R/L; #difference between two half power points\n",
+ "cosphi=R/R; #power factor at resonance\n",
+ "\n",
+ "#Result\n",
+ "print \"resonant frequency is\",omega0/10**5,\"*10**5 rad/sec\"\n",
+ "print \"power factor at resonance is\",cosphi"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "resonant frequency is 1.0 *10**5 rad/sec\n",
+ "power factor at resonance is 1.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.13, Page number 313"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "C=0.1*10**-6; #capacitance(F)\n",
+ "L=10*10**-3; #inductance(H)\n",
+ "R=10; #resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "Z=L/(C*R); #impedence at resonance(ohm)\n",
+ "\n",
+ "#Result\n",
+ "print \"impedence at resonance is\",Z/10**4,\"*10**4 ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "impedence at resonance is 1.0 *10**4 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 9.14, Page number 313"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "C=5*10**-6; #capacitance(F)\n",
+ "L=10*10**-3; #inductance(H)\n",
+ "R=10*10**3; #resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "omegar=1/math.sqrt(L*C); #resonant frequency(Hz)\n",
+ "omegar=round(omegar/10**3,1);\n",
+ "delta_omega=1/(R*C); #bandwidth(Hz)\n",
+ "Q=omegar*10**3/delta_omega; #Q-factor\n",
+ "\n",
+ "#Result\n",
+ "print \"resonant frequency is\",omegar,\"*10**3 Hz\"\n",
+ "print \"bandwidth is\",delta_omega,\"Hz\"\n",
+ "print \"Q-factor is\",Q"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "resonant frequency is 4.5 *10**3 Hz\n",
+ "bandwidth is 20.0 Hz\n",
+ "Q-factor is 225.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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