{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 7 - Basic Measuring Instruments"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1 - pg 7-13"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"deflection theta (deg) = 30.0\n"
]
}
],
"source": [
"#Chapter-7,Example7_1,pg 7-13\n",
"#calculate the deflection angle\n",
"#given\n",
"N=100.\n",
"B=0.15\n",
"A=10*8*10**-6\n",
"I=5*10**-3\n",
"K=0.2*10**-6#spring const.\n",
"#calculations\n",
"Td=N*B*A*I#deflecting torque\n",
"theta=Td/K#deflecting angle\n",
"#results\n",
"print\"deflection theta (deg) = \",theta"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 - pg 7_21"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"deflection for given current (degrees) = 144.75\n",
"inductance for given deflection (muH) = 2.53\n"
]
}
],
"source": [
"#Chapter-7,Example7_2,pg 7-21\n",
"#given\n",
"#calculate the deflection\n",
"import math\n",
"from sympy import *\n",
"x=Symbol('x')\n",
"L=(12+6*x-(x**2))#x is deflection in rad from zero\n",
"dl=L.diff(x)\n",
"K=12.\n",
"I=8.\n",
"#calculations\n",
"x=6./(((2*K)/(I**2))+2)#x=((I**2)dl)/(2*k)\n",
"z=x*(180./math.pi)\n",
"y=horner(x,L)\n",
"#results\n",
"print\"deflection for given current (degrees) = \",round(z,2)\n",
"print\"inductance for given deflection (muH) = \",round(y,2)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3 - pg 7_23"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"value of shunt resistance (ohm) = 1.351\n"
]
}
],
"source": [
"#Chapter-7,Example7_3,pg 7-23\n",
"#calculate the value of shunt resistance\n",
"#given\n",
"Rm=100.\n",
"Im=2.*10**-3\n",
"I=150.*10**-3\n",
"#calculations\n",
"Rsh=(Im*Rm)/(I-Im)\n",
"#results\n",
"print\"value of shunt resistance (ohm) = \",round(Rsh,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4 - pg 7_23"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"current through shunt (A) = 40.0\n",
"voltage through shunt (V) = 0.5\n",
"meter resistance (ohm) = 937.5\n"
]
}
],
"source": [
"#Chapter-7,Example7_4,pg 7-23\n",
"#calculate the current, voltage and meter resistance\n",
"#given\n",
"Vsh1=400.*10**-3\n",
"Rsh=0.01\n",
"Ish1=50.\n",
"Rm=750.#coil resistance\n",
"#calculations\n",
"Ish=Vsh1/Rsh\n",
"Vsh=Ish1*Rsh\n",
"Im=Vsh1/Rm\n",
"Rm1=Vsh/Im#meter resistance\n",
"#results\n",
"print\"current through shunt (A) = \",Ish\n",
"print\"voltage through shunt (V) = \",Vsh\n",
"print\"meter resistance (ohm) = \",Rm1\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5 - pg 7_25"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"designed multi-range ammeter\n",
"full scale deflection Im (mA) = 2.0\n",
"meter resistance Rm (ohm) = 75\n",
"R1(ohm) = 18.75\n",
"R2(ohm) = 3.125\n",
"R3(ohm) = 1.53\n"
]
}
],
"source": [
"#Chapter-7,Example7_5,pg 7-25\n",
"#calculate the full scale deflection and meter resistance\n",
"#given\n",
"I1=10*10**-3\n",
"Im=2*10**-3\n",
"Rm=75\n",
"I2=50*10**-3\n",
"I3=100*10**-3\n",
"#calculations\n",
"R1=(Im*Rm)/(I1-Im)\n",
"R2=(Im*Rm)/(I2-Im)\n",
"R3=(Im*Rm)/(I3-Im)\n",
"#results\n",
"print\"designed multi-range ammeter\"\n",
"print\"full scale deflection Im (mA) = \",Im*1000.\n",
"print\"meter resistance Rm (ohm) = \",Rm\n",
"print\"R1(ohm) = \",R1\n",
"print\"R2(ohm) = \",R2\n",
"print\"R3(ohm) = \",round(R3,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6 - pg 7_27"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"various sections of aryton shunt are\n",
"\n",
"full scale deflection Im (mA) = 1.0\n",
"meter resistance Rm (ohm) = 50.0\n",
"R1 (ohm) = 0.005\n",
"R2 (ohm) = 0.005\n",
"R3 (ohm) = 0.03999\n"
]
}
],
"source": [
"#Chapter-7,Example7_6,pg 7-27\n",
"#calculate the meter resistance and full scale deflection\n",
"#given\n",
"I1=10.\n",
"Im=1*10**-3\n",
"Rm=50.\n",
"#in position-1 R1 is in shunt with R2+R3+Rm\n",
"#R1=10**-4(R2+R3+50)......(1)\n",
"#in position-2 (R1+R2) is in shunt with R3+Rm\n",
"#R1+R2=2*10**-4(R3+50).....(2)\n",
"#in position-3 R1+R2+R3 is in shunt with Rm\n",
"#R1+R2+R3=0.05............(3)\n",
"#from.....(3)\n",
"#R1+R2=0.05-R3\n",
"#substituting in........(2)\n",
"#calculations\n",
"R3=0.04/1.0002\n",
"#R2=0.01-R1........(4)\n",
"#substituing in (1)\n",
"R1=5.00139*10**-3/1.0001\n",
"R2=0.01-R1#from........(4)\n",
"#results\n",
"print\"various sections of aryton shunt are\\n\"\n",
"print\"full scale deflection Im (mA) = \",Im*1000.\n",
"print\"meter resistance Rm (ohm) = \",Rm\n",
"print\"R1 (ohm) = \",round(R1,3)\n",
"print\"R2 (ohm) = \",round(R2,3)\n",
"print\"R3 (ohm) = \",round(R3,5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 7 - pg 7_30"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"multiplier resistance (kohm) = 249.5\n"
]
}
],
"source": [
"#Chapter-7,Example7_7,pg 7-30\n",
"#calculate the multiplier resistance\n",
"#given\n",
"Rm=500.\n",
"Im=40*10**-6\n",
"V=10\n",
"#calculations\n",
"Rs=(V/Im)-Rm\n",
"#results\n",
"print\"multiplier resistance (kohm) = \",Rs/1000.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 8 - pg 7_30"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"required shunt resistance (ohm) = 0.001\n",
"required multipler resistance (kohm) = 24.99\n"
]
}
],
"source": [
"#Chapter-7,Example7_8,pg 7-30\n",
"#calculate the required shunt and multipler resistances\n",
"#given\n",
"Im=20*10**-3\n",
"Vm=200*10**-3\n",
"I=200\n",
"#calculations\n",
"Rm=(Vm/Im)\n",
"Rsh=(Im*Rm)/(I-Im)\n",
"V=500.\n",
"Rs=(V/Im)-Rm\n",
"#results\n",
"print\"required shunt resistance (ohm) = \",round(Rsh,3)\n",
"print\"required multipler resistance (kohm) = \",Rs/1000.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9 - pg 7_33"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"series string of multipliers\n",
"R1 (kohm) = 200.0\n",
"R2 (kohm) = 25.0\n",
"R3 (kohm) = 20.0\n",
"R4 (kohm) = 4.95\n"
]
}
],
"source": [
"#Chapter-7,Example7_9,pg 7-33\n",
"#calculate the series string of multiplers\n",
"#given\n",
"Rm=50\n",
"Im=2*10**-3\n",
"#calculations\n",
"#for position V4 multipler is R4\n",
"V4=10.\n",
"R4=(V4/Im)-Rm#Rs=(V/Im)-RmV3 m\n",
"#for position V3 multipler is R3+R4\n",
"V3=50.\n",
"R3=(V3/Im)-Rm-R4\n",
"#for position V2 multiplier is R2+R3+R4\n",
"V2=100.\n",
"R2=(V2/Im)-Rm-R3-R4\n",
"#for position V1 multiplier is R1+R2+R3+R4\n",
"V1=500.\n",
"R1=(V1/Im)-Rm-R3-R4-R2\n",
"#results\n",
"print\"series string of multipliers\"\n",
"print\"R1 (kohm) = \",R1/1000.\n",
"print\"R2 (kohm) = \",R2/1000.\n",
"print\"R3 (kohm) = \",R3/1000.\n",
"print\"R4 (kohm) = \",R4/1000.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 10 - pg 7_35"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"series string of multipliers\n",
"R1 (ohm) = 200.0\n",
"R2 (ohm) = 25.0\n",
"R3 (ohm) = 20.0\n",
"R4 (ohm) = 4.95\n"
]
}
],
"source": [
"#Chapter-7,Example7_10,pg 7-35\n",
"#calculate the series string of multipliers\n",
"#given\n",
"Rm=50\n",
"Im=2*10**-3\n",
"V1=500.\n",
"V2=100.\n",
"V3=50.\n",
"V4=10.\n",
"#calculations\n",
"S=1/Im#senstivity\n",
"R4=S*V4-Rm\n",
"R3=S*V3-(R4+Rm)\n",
"R2=S*V2-(R4+Rm+R3)\n",
"R1=S*V1-(R4+Rm+R3+R2)\n",
"#results\n",
"print\"series string of multipliers\"\n",
"print\"R1 (ohm) = \",R1/1000.\n",
"print\"R2 (ohm) = \",R2/1000.\n",
"print\"R3 (ohm) = \",R3/1000.\n",
"print\"R4 (ohm) = \",R4/1000.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 11 - pg 7_36"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"multipler resistance (Mohm) = 9.9998\n"
]
}
],
"source": [
"#Chapter-7,Example7_11,pg 7-36\n",
"#calculate the multipler resistance\n",
"#given\n",
"Im=50*10**-6\n",
"Rm=200.\n",
"V=500.#V is voltage range\n",
"#calculations\n",
"S=1/Im\n",
"Rs=S*V-Rm\n",
"#results\n",
"print\"multipler resistance (Mohm) = \",round(Rs/10**6,4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 12 - pg 7_36"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"senstivity of meter A (ohm/volt) = 260.0\n",
"senstivity of meter B (ohm/volt) = 151.0\n",
"Meter A is more sensitive than meter B\n"
]
}
],
"source": [
"#calculate the senstivity of meters A and B\n",
"#Chapter-7,Example7_12,pg 7-36\n",
"#given\n",
"#for meter A\n",
"Rs=25.*10**3\n",
"Rm=1.*10**3\n",
"V=100.\n",
"#calculations\n",
"S=(Rs+Rm)/V\n",
"#for meter B\n",
"Rs=150.*10**3\n",
"Rm=1.*10**3\n",
"V=1000.\n",
"S2=(Rs+Rm)/V\n",
"#results\n",
"print\"senstivity of meter A (ohm/volt) = \",S\n",
"print\"senstivity of meter B (ohm/volt) = \",S2\n",
"print 'Meter A is more sensitive than meter B'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 13 - pg 7-37"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"first voltmeter reading (V) = 120.97\n",
"second voltmeter reading (V) = 137.87\n"
]
}
],
"source": [
"#Chapter-7,Example7_13,pg 7-37\n",
"#calculate the voltmeter readings\n",
"#given\n",
"R1=20.*10**3\n",
"R2=25.*10**3\n",
"V=250#voltage supply\n",
"#calculations and results\n",
"VR2=R2*V/(R1+R2)#voltage across R2\n",
"#case-1\n",
"S=500\n",
"Vr=150#voltage range of resistor\n",
"Rv=S*Vr\n",
"Req=R2*Rv/(R2+Rv)\n",
"VReq=Req*V/(Req+R1)#voltage across Req\n",
"print\"first voltmeter reading (V) = \",round(VReq,2)\n",
"#case-2\n",
"S=10*10**3\n",
"Rv=S*Vr\n",
"Req=R2*Rv/(R2+Rv)\n",
"VReq=Req*V/(Req+R1)\n",
"print\"second voltmeter reading (V) = \",round(VReq,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 14 - pg 7_38"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"true voltage (V) = 4.167\n",
"voltmeter reading case-1 (V) = 3.571\n",
"percentage error (percent) = 14.3\n",
"percentage accuracy = 85.7\n",
"voltmeter reading case-2 (V) = 4.132\n",
"percentage error (percent) = 0.83\n",
"percentage accuracy = 99.17\n"
]
}
],
"source": [
"#Chapter-7,Example7_14,pg 7-38\n",
"#calculate the voltmeter reading case and percentage error,accuracy\n",
"#given\n",
"Rb=1.*10**3\n",
"Ra=5.*10**3\n",
"V=25.\n",
"#calculations and results\n",
"VRb=Rb*V/(Ra+Rb)#voltage across Rb\n",
"Vr=5.\n",
"#case-1\n",
"S=1.*10**3\n",
"Rv=S*Vr\n",
"Req=Rb*Rv/(Rb+Rv)\n",
"VReq=Req*V/(Req+Ra)\n",
"err=(VRb-VReq)*100/VRb\n",
"acc=100-err\n",
"print \"true voltage (V) = \",round(VRb,3)\n",
"print\"voltmeter reading case-1 (V) = \",round(VReq,3)\n",
"print\"percentage error (percent) = \",round(err,1)\n",
"print\"percentage accuracy = \",round(acc,1)\n",
"#case-2\n",
"S=20*10**3\n",
"Rv=S*Vr\n",
"Req=Rb*Rv/(Rb+Rv)\n",
"VReq=Req*V/(Req+Ra)\n",
"err=(VRb-VReq)*100/VRb\n",
"acc=100-err\n",
"print\"voltmeter reading case-2 (V) = \",round(VReq,3)\n",
"print\"percentage error (percent) = \",round(err,2)\n",
"print\"percentage accuracy = \",round(acc,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 15 - pg 7_41"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"shunt resistance for I=10A (ohm) = 0.1002\n",
"shunt resistance for I=20A (ohm) = 0.05\n",
"series resistance for V=150V (kohm) = 7.45\n",
"series resistance for V=300V (kohm) = 14.95\n"
]
}
],
"source": [
"#Chapter-7,Example7_15,pg 7-41\n",
"#calculate the shunt and series resistances\n",
"#given\n",
"Rm=50.\n",
"Im=20.*10**-3\n",
"I=10.\n",
"#calculatiosn and results\n",
"Rsh=(Im*Rm)/(I-Im)\n",
"print\"shunt resistance for I=10A (ohm) = \",round(Rsh,4)\n",
"\n",
"I=20\n",
"Rsh=(Im*Rm)/(I-Im)\n",
"print\"shunt resistance for I=20A (ohm) = \",round(Rsh,2)\n",
"\n",
"V=150\n",
"Rs=(V/Im)-Rm\n",
"print\"series resistance for V=150V (kohm) = \",round(Rs/1000.,2)\n",
"\n",
"V=300\n",
"Rs=(V/Im)-Rm\n",
"print\"series resistance for V=300V (kohm) = \",round(Rs/1000.,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 16 - pg 7_42"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"shunt current (A) = 25.0\n",
"resistance for Ish=10A (ohm) = 400.0\n",
"resistance for Ish=75A (ohm) = 3000.0\n"
]
}
],
"source": [
"#Chapter-7,Example7_16,pg 7-42\n",
"#calculate the shunt current,resistance\n",
"#given\n",
"Rsh=0.02\n",
"R=1000.\n",
"Vm=500.*10**-3\n",
"#calculations and results\n",
"Im=Vm/R\n",
"Ish=Vm/Rsh\n",
"print\"shunt current (A) = \",Ish\n",
"Ish1=10.\n",
"V=Ish1*Rsh\n",
"R=V/Im\n",
"print\"resistance for Ish=10A (ohm) = \",R\n",
"Ish2=75.\n",
"V=Ish2*Rsh\n",
"R=V/Im\n",
"print\"resistance for Ish=75A (ohm) = \",R"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 17 - pg 7_50"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"final inductance (muH) = 4.0528\n"
]
}
],
"source": [
"#Chapter-7,Example7_17,pg 7-50\n",
"#calculate the final inductance\n",
"#given\n",
"import math\n",
"K=5.73*10**-6\n",
"I=20.\n",
"theta=110*(math.pi/180)#full scale deflection\n",
"L=4*10**-6\n",
"#calculations\n",
"dtheta=theta#change in theta\n",
"dm=(theta*K/(I**2))*dtheta#change in inductance\n",
"Lf=L+dm\n",
"#results\n",
"print\"final inductance (muH) = \",round(Lf*10**6,4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 18 - pg 7_50"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"deflecting torque (muNm) = 0.48296\n"
]
}
],
"source": [
"#Chapter-7,Example7_18,pg 7-50\n",
"#calculate the deflecting torque\n",
"import math\n",
"#given\n",
"I=10*10**-3\n",
"x=30#deflection\n",
"#calculations\n",
"dM=5*math.sin((x+45)*(math.pi/180))*10**-3#diffrentiate M w.r.t x\n",
"Td=(I**2)*dM#deflecting torque\n",
"#results\n",
"print\"deflecting torque (muNm) = \",round(Td*10**6,5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19 - pg 7_51"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"difference in readings Vdc=100V (V) = 1.2718\n",
"difference in readings Vdc=50V (V) = 0.6132\n"
]
}
],
"source": [
"#Chapter-7,Example7_19,pg 7-51\n",
"#calculate the difference in readings\n",
"import cmath\n",
"import math\n",
"#given\n",
"I=100*10**-3\n",
"Td=0.8*10**-4\n",
"dtheta=90*math.pi/180#in radians\n",
"theta=90#deflection\n",
"#calculations\n",
"dM=Td*dtheta/(I**2)\n",
"Mo=0.5#original M\n",
"M=Mo+dM#total M\n",
"#case-1 \n",
"Vdc=100\n",
"R=Vdc/I\n",
"w=2*math.pi*50\n",
"Z=R+(1j*w*M)\n",
"Z=abs(Z)\n",
"Vac=R*Vdc/Z\n",
"dif=Vdc-Vac#difference between readings\n",
"#case-2\n",
"Vdc1=50\n",
"I1=Vdc1/R\n",
"theta1=theta*((I1/I)**2)#theta=kI**2\n",
"theta1=theta1*math.pi/180#in radians\n",
"dM1=Td*theta1/(I**2)\n",
"M1=dM1+Mo\n",
"Z1=R+(1j*w*M1)\n",
"Z1=abs(Z1)\n",
"Vac1=R*Vdc1/Z1\n",
"dif1=Vdc1-Vac1\n",
"#results\n",
"print\"difference in readings Vdc=100V (V) = \",round(dif,4)\n",
"print\"difference in readings Vdc=50V (V) = \",round(dif1,4)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 20 - pg 7_65"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"percentage error = -2.174\n",
"negative sign shows that meter is slow and Er<Et\n"
]
}
],
"source": [
"#Chapter-7,Example7_20,pg 7-65\n",
"#calculate the percentage error\n",
"#given\n",
"I=20.\n",
"V=230.\n",
"Pf=0.8#power factor\n",
"t=3600.\n",
"K=100.\n",
"#calculations\n",
"Et=V*I*Pf*t\n",
"Et=Et/(3600*10**3)#in kWh\n",
"N=360.\n",
"Er=3.6#in kWh\n",
"err=(Er-Et)/Et\n",
"err=err*100\n",
"#results\n",
"print\"percentage error = \",round(err,3)\n",
"print\"negative sign shows that meter is slow and Er<Et\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exampe 21 - pg 7_65"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"percentage error = 0.819\n",
"positive sign shows that meter is fast and Er>Et\n"
]
}
],
"source": [
"#Chapter-7,Example7_21,pg 7-65\n",
"#calculate the percentage error\n",
"#given\n",
"K=1800.\n",
"V=230.\n",
"I=10.\n",
"Pf=1.#half load\n",
"Ihl=I/2.#half load current\n",
"t=138.\n",
"#calculations\n",
"Et=V*Ihl*Pf*t\n",
"Et=Et/(3600*10**3)\n",
"N=80#no. of revolutions\n",
"Er=N/K#in kWh\n",
"err=(Er-Et)/Et\n",
"err=err*100\n",
"#results\n",
"print\"percentage error = \",round(err,3)\n",
"print\"positive sign shows that meter is fast and Er>Et\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 22 - pg 7_66"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"meter constant (rev/kWh) = 400.0\n",
"power factor (lagging) = 0.8\n"
]
}
],
"source": [
"#Chapter-7,Example7_22,pg 7-66\n",
"#calculate the meter constant and power factor\n",
"#given\n",
"V=230.\n",
"I=4.\n",
"t=6.\n",
"Pf=1.\n",
"N=2208.\n",
"#calculations\n",
"Et=V*I*Pf*t\n",
"K=N/Et\n",
"V=230\n",
"I=5\n",
"t=4\n",
"N=1472\n",
"Et=V*I*Pf*t\n",
"Er=N/K\n",
"Pf=(Er/Et)\n",
"#results\n",
"print\"meter constant (rev/kWh) = \",K*1000\n",
"print\"power factor (lagging) = \",Pf\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 23 - pg 7_66"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"speed of disc (rpm) = 60.04\n",
"percentage error = 0.77\n",
"Er>Et meter is fast\n"
]
}
],
"source": [
"#Chapter-7,Example7_23,pg 7-66\n",
"#calculate the speed of disc and percentage error\n",
"#given\n",
"I=5.\n",
"V=220.\n",
"Pf=1.\n",
"K=3275.\n",
"t=1/60.#in hr\n",
"#calculations\n",
"E=V*I*Pf*t\n",
"E=E/10**3#in kWh\n",
"Rev=E*K#no. of revolutions\n",
"#at half load\n",
"I=I/2\n",
"t=59.5\n",
"Et=V*I*Pf*t\n",
"Et=Et/(3600*10**3)#in kWh\n",
"N=30\n",
"Er=N/K\n",
"err=(Er-Et)/Et\n",
"err=err*100.\n",
"print\"speed of disc (rpm) = \",round(Rev,2)\n",
"print\"percentage error = \",round(err,2)\n",
"print\"Er>Et meter is fast\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 24 - pg 7_67"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"in case 1, percentage error in case-1 = -0.2436\n",
"speed of disc (rpm) = 19.2\n",
"in case 2, percentage error in case-2 = -12.326\n"
]
}
],
"source": [
"#Chapter-7,Example7_24,pg 7-67\n",
"#calculate the speed and percentage error\n",
"import math\n",
"from math import cos,sin\n",
"#given\n",
"V=240.\n",
"I=10.\n",
"Pf=0.8\n",
"t=1/60.\n",
"K=600.\n",
"#calculations\n",
"E=V*I*Pf*t\n",
"E=E/10**3#in kWh\n",
"Rev=E*K#no. of revolutions \n",
"dela=90#for correct lag adjustment\n",
"dela1=86*math.pi/180#given in radian\n",
"phi=0#case-1 unity power factor\n",
"err=(sin(dela1-phi)-cos(phi))/cos(phi)\n",
"err=err*100\n",
"print\"in case 1, percentage error in case-1 = \",round(err,4)\n",
"Pf=0.5#case-2\n",
"phi=60*math.pi/180#in radians\n",
"err=(sin(dela1-phi)-cos(phi))/cos(phi)\n",
"err=err*100\n",
"print\"speed of disc (rpm) = \",Rev\n",
"print\"in case 2, percentage error in case-2 = \",round(err,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 25 - pg 7_67"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"percentage error upperlimt = 0.07\n",
"percentage error lowerlimt = 0.331\n"
]
}
],
"source": [
"#Chapter-7,Example7_25,pg 7-67\n",
"#calculate the percentage error upperlimt and lowerlimt\n",
"#given\n",
"V=240.\n",
"I=5.\n",
"K=1200.\n",
"N=40.\n",
"t=99.8\n",
"Td=500#total divisions\n",
"#calculations\n",
"Er=N/K\n",
"W=V*I\n",
"div=K/Td#1 division\n",
"We=0.1*div#wattmeter error\n",
"Ce=0.05*K/100#construction wattmeter error\n",
"Te=We+Ce#total error\n",
"Wru=K+Te\n",
"Wrl=K-Te#wattmeter reading limits\n",
"He=0.05#human error\n",
"Se=0.01#stopwatch error\n",
"Tte=He+Se#total timing error\n",
"Sru=t+Tte#stopwatch reading limits\n",
"Srl=t-Tte\n",
"Eu=Wru*Sru*1/(3600*10**3)#energy obtained limits\n",
"El=Wrl*Srl*1/(3600*10**3)\n",
"errl=(Er-El)/El\n",
"errl=errl*100\n",
"erru=(Er-Eu)/Eu#error limits\n",
"erru=erru*100\n",
"#results\n",
"print\"percentage error upperlimt = \",round(erru,3)\n",
"print\"percentage error lowerlimt = \",round(errl,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 26 - pg 7_79"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"line current (A) = 135.0\n"
]
}
],
"source": [
"#Chapter-7,Example7_26,pg 7-79\n",
"#calculate the line current\n",
"#given\n",
"I1=250.\n",
"I2=5.\n",
"#calculations\n",
"I=I1/I2\n",
"#as ammeter is in secondary I2=2.7\n",
"I1=I*2.7#line current\n",
"#results\n",
"print\"line current (A) = \",I1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 27 - pg 7_82"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"line voltage (V) = 8750.0\n"
]
}
],
"source": [
"#Chapter-7,Example7_27,pg 7-82\n",
"#calculate the line voltage\n",
"#given\n",
"V1=11000.\n",
"V2=110.\n",
"#calculations\n",
"V=V1/V2\n",
"V2=87.5\n",
"V1=87.5*V#line voltage\n",
"#results\n",
"print\"line voltage (V) = \",V1\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 28 - pg 7_88"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"percentage ratio error = -3.66\n"
]
}
],
"source": [
"#Chapter-7,Example7_28,pg 7-88\n",
"#calculate the percentage ratio error\n",
"#given\n",
"Im=120.\n",
"Ic=38.\n",
"Kn=1000./5 #at full load\n",
"Is=5.\n",
"Ns=1000.\n",
"Np=5.\n",
"#calculations\n",
"n=Ns/Np#turns ratio\n",
"R=n+(Ic/Is)\n",
"err=(Kn-R)/R#ratio error\n",
"err=err*100.\n",
"#results\n",
"print\"percentage ratio error = \",round(err,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 29 - pg 7_88"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"percentage ratio error = -3.734\n"
]
}
],
"source": [
"#Chapter-7,Example7_29,pg 7-88\n",
"#calculate the percentage ratio error\n",
"#given\n",
"import math\n",
"Im=90.\n",
"Ic=40.\n",
"delta=28*(math.pi/180)#in radians\n",
"Is=5.\n",
"Ns=400.\n",
"Np=1.\n",
"#calculations\n",
"n=Ns/Np\n",
"Kn=n\n",
"R=n+((Im*math.sin(delta)+Ic*math.cos(delta))/Is)\n",
"Ip=R*Is#actual primary current\n",
"err=(Kn-R)/R\n",
"err=err*100\n",
"#results\n",
"print\"percentage ratio error = \",round(err,3)\n"
]
}
],
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