{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 5: Series and parallel\n", "networks

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 1, page no. 43

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine (a) the battery voltage V, (b) the total resistance of the circuit, and \n", "#(c) the values of resistance of resistors R1, R2 and R3,\n", "from __future__ import division\n", "#initializing the variables:\n", "V1 = 5; # in volts\n", "V2 = 2; # in volts\n", "V3 = 6; # in volts\n", "I = 4; # in Amperes\n", "\n", "#calculation:\n", "Vt = V1 + V2 + V3\n", "Rt = Vt/I\n", "R1 = V1/I\n", "R2 = V2/I\n", "R3 = V3/I\n", "\n", "#results\n", "print \"(a) Total Voltage\", Vt,\"Volts(V)\"\n", "print \"(b)Total Resistance\", Rt,\"Ohms\"\n", "print \"(c)Resistance(R1)\", R1,\"Ohms; Resistance(R2)\", R2,\"Ohms and\"\n", "print \"Resistance(R3)\", R3,\"Ohms\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Total Voltage 13 Volts(V)\n", "(b)Total Resistance 3.25 Ohms\n", "(c)Resistance(R1) 1.25 Ohms; Resistance(R2) 0.5 Ohms and\n", "Resistance(R3) 1.5 Ohms" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 2, page no. 43

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine the p.d. across resistor R3.\n", "#Find value of resistor R2\n", "from __future__ import division\n", "#initializing the variables:\n", "V1 = 10; # in volts\n", "V2 = 4; # in volts\n", "Vt = 25; # in volts\n", "Rt = 100; # in ohms\n", "\n", "#calculation:\n", "V3 = Vt - V1 - V2\n", "I = Vt/Rt\n", "R2 = V2/I\n", "\n", "#results\n", "print \"(a)Voltage(V3)\", V3,\"Volts(V)\"\n", "print \"(b)current\", I,\"Amperes(A)\"\n", "print \"(c)Resistance(R2)\", R2,\"Ohms\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)Voltage(V3) 11 Volts(V)\n", "(b)current 0.25 Amperes(A)\n", "(c)Resistance(R2) 16.0 Ohms" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 3, page no. 44

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the current flowing through, and the p.d. across the 9 ohm resistor. \n", "#Find also the power dissipated in the 11 ohm resistor.\n", "from __future__ import division\n", "#initializing the variables:\n", "Vt = 12; # in volts\n", "R1 = 4; # in ohms\n", "R2 = 9; # in ohms\n", "R3 = 11; # in ohms\n", "\n", "#calculation:\n", "Rt = R1 + R2 + R3\n", "I = Vt/Rt\n", "V9 = I*R2\n", "P11 = I*I*R3\n", "#results\n", "print \"a)current\", I,\"Amperes(A)\\n\"\n", "print \"b)Voltage(V2)\", V9,\"Volts(V)\\n\"\n", "print \"c)Power\", P11,\"Watt(W)\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a)current 0.5 Amperes(A)\n", "\n", "b)Voltage(V2) 4.5 Volts(V)\n", "\n", "c)Power 2.75 Watt(W)" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 4, page no. 44

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the value of voltage V\n", "from __future__ import division\n", "#initializing the variables:\n", "Vt = 50; # in volts\n", "R1 = 4; # in ohms\n", "R2 = 6; # in ohms\n", "\n", "#calculation:\n", "Rt = R1 + R2\n", "I = Vt/Rt\n", "V2 = I*R2\n", "\n", "#results\n", "print \"Voltage(V)\", V2,\"Volts(V)\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Voltage(V) 30.0 Volts(V)" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5, page no. 45

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine (a) the value of the other resistor, and \n", "#(b) the p.d. across the 2 \u0006 resistor. \n", "#If the circuit is connected for 50 hours, how much energy is used?\n", "from __future__ import division\n", "#initializing the variables:\n", "Vt = 24; # in volts\n", "R1 = 2; # in ohms\n", "I = 3; # in Amperes\n", "t = 50; # in hrs\n", "\n", "#calculation:\n", "V1 = I*R1\n", "R2 = (Vt-(I*R1))/I\n", "E = Vt*I*t\n", "\n", "#results\n", "print \"a)Voltage(V1)\", V1,\"Volts(V)\\n\"\n", "print \"b)Resistance(R2)\", R2,\"Ohms\\n\"\n", "print \"c)Energy(E)\", E/1000,\"kWh\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a)Voltage(V1) 6 Volts(V)\n", "\n", "b)Resistance(R2) 6.0 Ohms\n", "\n", "c)Energy(E) 3.6 kWh" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 6, page no. 46

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine (a) the reading on the ammeter, and \n", "# (b) the value of resistor R2\n", "from __future__ import division\n", "#initializing the variables:\n", "R1 = 5; # in ohms\n", "R3 = 20; # in ohms\n", "I1 = 8; # in Amperes\n", "It = 11; # in Amperes\n", "\n", "#calculation:\n", "Vt = I1*R1\n", "I3 = Vt/R3\n", "R2 = Vt/(It - I1 - I3)\n", "\n", "#results\n", "print \"a)Ammeter Reading\", I3,\"Amperes(A)\\n\"\n", "print \"b)Resistance(R2)\", R2,\"Ohms\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a)Ammeter Reading 2.0 Amperes(A)\n", "\n", "b)Resistance(R2) 40.0 Ohms" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 7, page no. 46

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine (a) the total circuit resistance and (b) the current flowing in the 3 ohm resistor.\n", "from __future__ import division\n", "#initializing the variables:\n", "R1 = 3; # in ohms\n", "R2 = 6; # in ohms\n", "Vt = 12; # in volts\n", "\n", "#calculation:\n", "Rt = R1*R2/(R1 + R2)\n", "I1 = (Vt/R1)\n", "\n", "#Result\n", "print \"(a)Total Resistance\", Rt,\"Ohms\\n\"\n", "print \"(b)Current(I1)\", I1,\"Amperes(A)\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)Total Resistance 2.0 Ohms\n", "\n", "(b)Current(I1) 4.0 Amperes(A)" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8, page no. 47

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#find (a) the value of the supply voltage V and (b) the value of current I.\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "R1 = 10;# in ohms\n", "R2 = 20;# in ohms\n", "R3 = 60;# in ohms\n", "I2 = 3;# in Amperes\n", "\n", "#calculation:\n", "Vt = I2*R2\n", "I1 = Vt/R1\n", "I3 = Vt/R3\n", "I = I1 +I2 + I3\n", "\n", "print \"\\nResult\\n\"\n", "print \"\\n(a)Voltage(V) \",Vt,\" Volts(V)\\n\"\n", "print \"\\n(b)Total Current(I) \",I,\" Amperes(A)\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Result\n", "\n", "\n", "(a)Voltage(V) 60 Volts(V)\n", "\n", "\n", "(b)Total Current(I) 10.0 Amperes(A)" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 9, page no. 47

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#state how they must be connected to give an overall resistance of \n", "#(a) 1/4 ohm (b) 1 ohm (c) 4/3 ohm (d)2.5 ohm, all four resistors being connected in each case\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "R = 1;# in ohms\n", "\n", "#calculation\n", "R1 = 1/(1/R + 1/R + 1/R + 1/R)\n", "R2 = 2*R*2*R/(4*R)\n", "R3 = 1/(1/R + 1/R + 1/R) + 1\n", "R4 = R*R/(2*R) + 2*R\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n(a)All four in parallel for \",R1,\" ohm\\n\"\n", "print \"\\n(b)Two in series, in parallel with another two in series for\",R2,\" ohm\\n\"\n", "print \"\\n(c)Three in parallel, in series with one for \",round(R3,2),\" ohm\\n\"\n", "print \"\\n(d)Two in parallel, in series with two in series for \",R4,\" ohm\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", "(a)All four in parallel for 0.25 ohm\n", "\n", "\n", "(b)Two in series, in parallel with another two in series for 1.0 ohm\n", "\n", "\n", "(c)Three in parallel, in series with one for 1.33 ohm\n", "\n", "\n", "(d)Two in parallel, in series with two in series for 2.5 ohm\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 10, page no. 48

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Find the equivalent resistance for the circuit\n", "from __future__ import division\n", "#initializing the variables:\n", "R1 = 1;# in ohms\n", "R2 = 2.2;# in ohms\n", "R3 = 3;# in ohms\n", "R4 = 6;# in ohms\n", "R5 = 18;# in ohms\n", "R6 = 4;# in ohms\n", "\n", "\n", "#calculation:\n", "R0 = 1/((1/3) + (1/6) + (1/18))\n", "Rt = R1 + R2 + R0 + R6\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n Equivalent Resistance \",Rt,\" Ohms\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", " Equivalent Resistance 9.0 Ohms" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11, page no. 48

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#find (a) the supply current, (b) the current flowing through each resistor and (c) the p.d. across each resistor.\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "R1 = 2.5;# in ohms\n", "R2 = 6;# in ohms\n", "R3 = 2;# in ohms\n", "R4 = 4;# in ohms\n", "Vt = 200;# in volts\n", "\n", "#calculation:\n", "R0 = 1/((1/R2) + (1/R3))\n", "Rt = R1 + R0 + R4\n", "It = Vt/Rt\n", "I1 = It\n", "I4 = It\n", "I2 = R3*It/(R3+R2)\n", "I3 = It - I2\n", "V1 = I1*R1\n", "V2 = I2*R2\n", "V3 = I3*R3\n", "V4 = I4*R4\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n (a)Total Current Supply \",It,\" Amperes(A)\\n\"\n", "print \"\\n (b)Current through resistors (R1, R2, R3, R4)\\n \",I1,\", \", I2,\", \", I3,\", \", I4,\" Amperes(A) respectively\\n\"\n", "print \"\\n (c)voltage across resistors (R1, R2, R3, R4)\\n \",V1,\", \", V2,\", \", V3,\", \", V4,\" Volts(V) respectively\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", " (a)Total Current Supply 25.0 Amperes(A)\n", "\n", "\n", " (b)Current through resistors (R1, R2, R3, R4)\n", " 25.0 , 6.25 , 18.75 , 25.0 Amperes(A) respectively\n", "\n", "\n", " (c)voltage across resistors (R1, R2, R3, R4)\n", " 62.5 , 37.5 , 37.5 , 100.0 Volts(V) respectively" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 12, page no. 49

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#calculate (a) the value of resistor Rx such that the total power dissipated in the circuit is 2.5 kW, and \n", "#(b) the current flowing in each of the four resistors\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "R1 = 15;# in ohms\n", "R2 = 10;# in ohms\n", "R3 = 38;# in ohms\n", "Vt = 250;# in volts\n", "P = 2500;# in Watt\n", "\n", "#calculation:\n", "It = P/Vt\n", "I2 = R1*It/(R1+R2)\n", "I1 = It - I2\n", "Re1 = 1/((1/R1) + (1/R2))\n", "Rt = Vt/It\n", "Re2 = Rt - Re1\n", "Rx = 1/((1/Re2) - (1/R3))\n", "I4 = R3*It/(R3+Rx)\n", "I3 = It - I4\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n (a)Resistance (Rx) \",Rx,\" Ohms\\n\"\n", "print \"\\n (b)Current through resistors (R1, R2, R3, R4): \\n \",I1,\", \", I2,\", \", I3,\", \"\n", "print \", I4,\" Amperes(A) respectively\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", " (a)Resistance (Rx) 38.0 Ohms\n", "\n", "\n", " (b)Current through resistors (R1, R2, R3, R4): \n", " 4.0 , 6.0 , 5.0 , 5.0 Amperes(A) respectively" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 13, page no. 51

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#find the current Ix\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "R1 = 8;# in ohms\n", "R2 = 2;# in ohms\n", "R3 = 1.4;# in ohms\n", "R4 = 9;# in ohms\n", "R5 = 2;# in ohms\n", "Vt = 17;# in volts\n", "\n", "#calculation:\n", "R01 = R1*R2/(R1 + R2)\n", "R02 = R01 + R3\n", "R03 = R4*R02/(R4 +R02)\n", "Rt = R5 + R03\n", "It = Vt/Rt\n", "I1 = R4*It/(R4 + R02)\n", "Ix = R2*I1/(R1 + R2)\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n Current(Ix) \",Ix,\" Amperes(A)\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", " Current(Ix) 0.6 Amperes(A)" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 14, page no. 52

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#find the resistance of one lamp.\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "Rt = 150;# in ohms\n", "n = 3;# no. of identical lamp\n", "\n", "#calculation:\n", "R = Rt*3# (1/Rt)=(1/R)+(1/R)+(1/R)\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n Resistance \",R,\" Ohms\\n\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", " Resistance 450 Ohms" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 15, page no. 52

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#State (a) the voltage across each lamp,\n", "# and (b) the effect of lamp C failing.\n", "from __future__ import division\n", "import math\n", "#initializing the variables:\n", "#series connection\n", "n = 3;# no. of identical lamp\n", "Vt = 150;# in volts\n", "\n", "#calculation:\n", "V = Vt/3# Since each lamp is identical, then V volts across each.\n", "\n", "print \"\\n\\nResult\\n\\n\"\n", "print \"\\n a)Voltage across each resistor = \",V,\" Volts(V)\\n\"\n", "print \"\\n b)If lamp C fails, i.e., open circuits, no current will flow and lamps A and B will not operate.\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Result\n", "\n", "\n", "\n", " a)Voltage across each resistor = 50.0 Volts(V)\n", "\n", "\n", " b)If lamp C fails, i.e., open circuits, no current will flow and lamps A and B will not operate." ] } ], "prompt_number": 21 } ], "metadata": {} } ] }