{
"metadata": {
"name": "",
"signature": "sha256:3ec304c8c9eb23fdd2ae23967a8effd62df3acdefa633ca8bf2a83485250a21b"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7 Electrical Measurements"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1 Page no 229"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"R1=2\n",
"R2=3\n",
"R3=5\n",
"E1=6\n",
"E2=4\n",
"\n",
"#Calculation\n",
"import math\n",
"A=np.array([[7,5],[5,8]])\n",
"b=np.array([6,4])\n",
"z=np.linalg.solve(A,b)\n",
"Z=z[0]\n",
"Z1=z[1]\n",
"A1=Z+Z1\n",
"\n",
"#Result\n",
"print\"Current through R1 is\", round(Z,3),\"A\"\n",
"print\"Current through R2 is\", round(Z1,3),\"A\"\n",
"print\"Current through R3 is\",round(A1,2),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current through R1 is 0.903 A\n",
"Current through R2 is -0.065 A\n",
"Current through R3 is 0.84 A\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2 Page no 229"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"E1=1.5 #V\n",
"E2=2.0 #V\n",
"r1=1 #ohm\n",
"r2=2 #ohm\n",
"R=5 #ohm\n",
"\n",
"#Calculation\n",
"import math\n",
"A=np.array([[6,5],[5,7]])\n",
"B=np.array([1.5,2])\n",
"Z=np.linalg.solve(A,B)\n",
"Z1=Z[0]\n",
"Z2=Z[1]\n",
"A1=(Z1+Z2)*R\n",
"\n",
"#Result\n",
"print\"Current through R1 is\", round(Z1,4),\"A\"\n",
"print\"Current through R2 is\",round(Z2,4),\"A\"\n",
"print\"Current through R3 is\",round(A1,4),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current through R1 is 0.0294 A\n",
"Current through R2 is 0.2647 A\n",
"Current through R3 is 1.4706 A\n"
]
}
],
"prompt_number": 42
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3 Page no 230"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"E1=2 #V\n",
"E2=1 #V\n",
"E3=4 #V\n",
"r1=4 #ohm\n",
"r2=3 #ohm\n",
"r3=2 #ohm\n",
"\n",
"#Calculation\n",
"import math\n",
"A=np.array([[1,1,1],[4,-3,0],[0,3,-2]])\n",
"A1=np.array([0,1,-3])\n",
"Z=np.linalg.solve(A,A1)\n",
"Z1=Z[0]\n",
"Z2=Z[1]\n",
"Z3=Z[2]\n",
"\n",
"#Result\n",
"print\"Current through R1 is\", round(Z1,2),\"A\"\n",
"print\"Current through R2 is\",round(Z2,2),\"A\"\n",
"print\"Current through R3 is\",round(Z3,2),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current through R1 is -0.15 A\n",
"Current through R2 is -0.54 A\n",
"Current through R3 is 0.69 A\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4 Page no 230"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"R1=5 #ohm\n",
"R3=2 \n",
"R=10\n",
"\n",
"#Calculation\n",
"import math\n",
"A=np.array([[9,5],[10,19]])\n",
"A1=np.array([1,1])\n",
"Z=np.linalg.solve(A,A1)\n",
"Z1=Z[0]\n",
"Z2=Z[1]\n",
"I=(Z1+Z2)*R\n",
"\n",
"#Result\n",
"print\"Potential difference across the resistor is\", round(I,4),\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Potential difference across the resistor is 1.0744 V\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5 Page no 230"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"A=10 #ohm\n",
"B=5 #ohm\n",
"S=2\n",
"\n",
"#Calculation\n",
"import math\n",
"A=np.array([[25,-10],[5,5]])\n",
"B=np.array([9,7]) \n",
"Z=np.linalg.solve(A,B)\n",
"Z1=Z[1]*10\n",
"\n",
"#Result\n",
"print\"Equivalent resistance is\", round(Z1,0),\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent resistance is 7.0 ohm\n"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6 Page no 231 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"P=15 #ohm\n",
"Q=12.0\n",
"R=10.0\n",
"S=4\n",
"\n",
"#Calculation\n",
"R1=S*(P/Q)\n",
"X=1/(1/R1-1/R)\n",
"\n",
"#Result\n",
"print\"The resistance to be connectedin parallel is\",X,\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The resistance to be connectedin parallel is 10.0 ohm\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7 Page no 231"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"P=4.0\n",
"Q=4.0\n",
"R=4.0\n",
"X=4.0\n",
"\n",
"#Calculation\n",
"R1=P+Q\n",
"R2=R+X\n",
"R3=1/(1/R1+1/R2)\n",
"I=P/R3\n",
"I1=I/2\n",
"\n",
"#Result\n",
"print\"(i) Equivalent resistance is\",R3,\"ohm\"\n",
"print\"(ii) The magnitudes of current is\",I1,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Equivalent resistance is 4.0 ohm\n",
"(ii) The magnitudes of current is 0.5 A\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.8 Page no 232"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=4\n",
"b=3\n",
"c=2.0\n",
"E=6 #v\n",
"\n",
"#Calculation\n",
"X=(a*b)/c\n",
"R1=a+c\n",
"R2=b+R1\n",
"R=((R1*R2)/(R1+R2))+2.4\n",
"I=E/R\n",
"\n",
"#Result\n",
"print\"Current drawn by the circuit is\", I,\"A\"\n",
"print\"Unknown resistance is\",R,\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current drawn by the circuit is 1.0 A\n",
"Unknown resistance is 6.0 ohm\n"
]
}
],
"prompt_number": 59
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9 Page no 232"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=1.5\n",
"b=5\n",
"c=6\n",
"\n",
"#Calculation\n",
"I1=a/(b+c)\n",
"I2=I1/10.0\n",
"I=I1+I2\n",
"\n",
"#Result\n",
"print\"Current in the arms is\", round(I1,4),\"A and\",round(I2,4),\"A\"\n",
"print\"Current in the cell is\",I,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current in the arms is 0.1364 A and 0.0136 A\n",
"Current in the cell is 0.15 A\n"
]
}
],
"prompt_number": 68
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10 Page no 233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"X=10\n",
"P=3\n",
"Q=2.0\n",
"\n",
"#Calculation\n",
"R=X*P/Q\n",
"L=1/R\n",
"\n",
"#Result\n",
"print\"Length is\",round(L,3),\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length is 0.067 m\n"
]
}
],
"prompt_number": 71
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11 Page no 233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"r=6 #ohm\n",
"l=1/3.0\n",
"r1=2/3.0\n",
"\n",
"#Calculation\n",
"R1=r/((2.0*(r1/l))-1)\n",
"R2=2*R1\n",
"\n",
"#Result\n",
"print\"Resistance of two wires is\", R1,\"ohm and\",R2,\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resistance of two wires is 2.0 ohm and 4.0 ohm\n"
]
}
],
"prompt_number": 76
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.12 Page no 233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"P=1.2 #ohm\n",
"Q=0.8\n",
"R=2\n",
"E=4 #V\n",
"\n",
"#Calculation\n",
"X=(R*P)/Q\n",
"R1=X+R\n",
"R2=P+Q\n",
"R11=R1*R2/(R1+R2)\n",
"I=E/R11\n",
"\n",
"#Result\n",
"print\"Unknown resistance is\", X,\"ohm\"\n",
"print\"Current drawn is\",I,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Unknown resistance is 3.0 ohm\n",
"Current drawn is 2.8 A\n"
]
}
],
"prompt_number": 83
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.13 Page no 233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"R=20.0 #ohm\n",
"V=10**-3 #V/m\n",
"l=10**4 #mm\n",
"V1=10**-2 #V\n",
"\n",
"#Calculation\n",
"I=V1/R\n",
"R1=(2/I)-R\n",
"\n",
"#Result\n",
"print\"Value of resistance is\", R1,\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of resistance is 3980.0 ohm\n"
]
}
],
"prompt_number": 87
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.14 Page no 233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"l1=65 #cm\n",
"l2=60.0\n",
"a=0.1\n",
"\n",
"#Calculation\n",
"E1=((a*l1)/l2)/((l1/l2)-1)\n",
"E2=E1-a\n",
"\n",
"#Result\n",
"print\"E.m.f of cell is\", E1,\"V and\",E2,\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"E.m.f of cell is 1.3 V and 1.2 V\n"
]
}
],
"prompt_number": 93
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.15 Page no 234"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"S=9.5 #ohm\n",
"I1=76.3 #cm\n",
"l2=64.8\n",
"\n",
"#Calculation\n",
"r=((I1/I2)-1)*S\n",
"\n",
"#Result\n",
"print\"Internal resistance is\",round(r*10**-3,1),\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Internal resistance is 53.1 ohm\n"
]
}
],
"prompt_number": 138
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.16 Page no 234"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"E=10*10**-3 \n",
"r=10\n",
"l=40 #cm\n",
"\n",
"#Calculation\n",
"R=10*l/100.0\n",
"R1=(R*2/E)-10\n",
"\n",
"#Result\n",
"print\"External resistance is\", R1,\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"External resistance is 790.0 ohm\n"
]
}
],
"prompt_number": 111
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.17 Page no 234"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"R1=10*10**3\n",
"E=12\n",
"\n",
"#Calculation\n",
"R=R1/((E/2.0)-1)\n",
"\n",
"#Result\n",
"print\"(a) Resistance is\",R*10**-3,\"K ohm\"\n",
"print\"(b) When current flows through a resistor,its temperature increases due toheat produced across it.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Resistance is 2.0 K ohm\n",
"(b) When current flows through a resistor,its temperature increases due toheat produced across it.\n"
]
}
],
"prompt_number": 116
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.18 Page no 235"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=3.0\n",
"b=6.0\n",
"\n",
"#Caculation\n",
"E=(1/a)+(1/b)+1+(1/a)\n",
"\n",
"#Result\n",
"print\"Equivalent resistance is\",round(E,2),\"r\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent resistance is 1.83 r\n"
]
}
],
"prompt_number": 120
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.22 Page no 237"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"a=5\n",
"b=10\n",
"\n",
"#Calculation\n",
"import math\n",
"A=np.array([[7,1],[1,5]])\n",
"A1=np.array([2,2])\n",
"B=np.linalg.solve(A,A1)\n",
"B1=B[0]\n",
"B2=B[1]\n",
"E=(a*B2)+(B1*b)\n",
"\n",
"#Result\n",
"print\"Equivalent resistance is\", round(E,2),\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent resistance is 4.12 ohm\n"
]
}
],
"prompt_number": 125
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.23 Page no 238"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"R=12.5\n",
"l=39.5\n",
"\n",
"#Calculation\n",
"X=(R*(100-l))/l\n",
"L=X/(X+R)\n",
"\n",
"#Result\n",
"print\"(a) Resistance is\",round(X,2),\"W\"\n",
"print\"(b) Balance point of bridge is\", L*10**2,\"cm\"\n",
"print\"(c) The galvanometer will not show any current.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Resistance is 19.15 W\n",
"(b) Balance point of bridge is 60.5 cm\n",
"(c) The galvanometer will not show any current.\n"
]
}
],
"prompt_number": 135
}
],
"metadata": {}
}
]
}