{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 3 - AC to DC Converters"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.1 page 117"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Power delivered = 199.11 W\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"R=100 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha=45 # degree\n",
"\n",
"Vo=Vs*sqrt(2)/2/pi*(1+cos(pi/180*alpha)) # V\n",
"Io=Vo/R # A\n",
"Vor=Vs/sqrt(2)*sqrt(1/180*((180-alpha)+sin(pi/180*2*alpha)/2)) # V\n",
"Ior=Vor/R # A\n",
"P=Ior**2*R # W\n",
"print 'Power delivered = %.2f W'%(P)\n",
"\n",
"#Ans in the textbook is not accurate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.2 page 118"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Power supplied to battery = 593 W\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,asin,cos,sin\n",
"\n",
"R=10 # ohm\n",
"E=165 # V\n",
"#vt=330*sin(314*t)\n",
"Vm=330 # V\n",
"f=314/2/pi # Hz\n",
"alpha1=asin(E/Vm) # radian\n",
"alpha2=pi-alpha1 # radian\n",
"Io=1/2/pi/R*(2*Vm*cos(alpha1)-E*(alpha2-alpha1)) # A\n",
"P=E*Io # W\n",
"\n",
"print 'Power supplied to battery = %d W'%(P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.3 page 119"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part (a)\n",
"\n",
" dc voltage Vo = 88.3 V\n",
"\n",
" & Current Io = 4.415 A\n",
"\n",
"\n",
" part (b)\n",
"\n",
" rms voltage Vor = 154.943 V\n",
"\n",
" & Current Ior = 7.747 A\n",
"\n",
"\n",
" part (c)\n",
"\n",
" dc Power = 389.85 W\n",
"\n",
" ac Power = 1200.37 W\n",
"\n",
" Rectification efficiency = 0.3248\n",
"\n",
"\n",
" part (d)\n",
"\n",
" Form factor = 1.755 \n",
"\n",
" Ripple factor = 1.442 \n",
"\n",
"\n",
" part (e)\n",
"\n",
" VA rating = 1781.8 VA\n",
"\n",
" Transformer Utilization factor = 0.2188\n",
"\n",
"\n",
" part (f)\n",
"\n",
" Peak inverse voltage = 325 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"#v2t = 325*sin(w*t)\n",
"R=20 # ohm\n",
"alfa=45 # degree\n",
"vm=325 # V\n",
"V=230 # V\n",
"print 'part (a)\\n'\n",
"Vo=vm/2/pi*(1+cos(pi/180*alfa)) # V\n",
"Io=Vo/R # A\n",
"print ' dc voltage Vo = %.1f V'%(Vo)\n",
"print '\\n & Current Io = %.3f A'%(Io)\n",
"print '\\n\\n part (b)\\n'\n",
"Vor=vm/2/sqrt(pi)*sqrt((pi-pi/180*alfa)+1/2*sin(pi/180*2*alfa)) # V\n",
"Ior=Vor/R # A\n",
"print ' rms voltage Vor = %.3f V'%(Vor)\n",
"print '\\n & Current Ior = %.3f A'%(Ior)\n",
"print '\\n\\n part (c)'\n",
"Pdc=Vo*Io # W\n",
"Pac=Vor*Ior # W\n",
"eta=Pdc/Pac # rectification efficiency\n",
"print \"\\n dc Power = %.2f W\"%(Pdc)\n",
"print \"\\n ac Power = %.2f W\"%(Pac)\n",
"print \"\\n Rectification efficiency = %.4f\"% (eta)\n",
"print '\\n\\n part (d)'\n",
"FF=Vor/Vo # form factor\n",
"RF=sqrt(FF**2-1)\n",
"print '\\n Form factor = %.3f '%(FF)\n",
"print '\\n Ripple factor = %.3f '%(RF)\n",
"print '\\n\\n part (e)'\n",
"VA=V*Ior # VA\n",
"TUF=Pdc/V/Ior # Transformer Utilization factor\n",
"print \"\\n VA rating = %.1f VA\"%(VA)\n",
"print \"\\n Transformer Utilization factor = %.4f\"%TUF\n",
"print '\\n\\n part (f)'\n",
"Vp=vm # V\n",
"print \"\\n Peak inverse voltage = %d V\"%Vp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.4 page 120"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a) Average value of current = 3.60 A\n",
"\n",
" (b) Power supplied to battery = 593 W\n",
"\n",
" (c) Power dissipated in the resistor = 1216.14 W\n",
"\n",
" (d) Power factor = 0.7043\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin,asin\n",
"\n",
"R=10 # ohm\n",
"E=165 # V\n",
"#vt=330*sin(314*t)\n",
"Vm=330 # V\n",
"Vs=233 # V\n",
"f=314/2/pi # Hz\n",
"theta1=asin(E/Vm) # radian\n",
"#alpha2=pi-alpha1 # radian\n",
"Io=1/2/pi/R*(2*Vm*cos(theta1)-E*(pi-2*theta1)) # A\n",
"print '(a) Average value of current = %.2f A'%(Io)\n",
"P=E*Io # W\n",
"print '\\n (b) Power supplied to battery = %d W'%(P)\n",
"Ior=sqrt(1/2/pi/R**2*((pi-2*theta1)*(Vs**2+E**2)+Vm**2*sin(2*theta1)-4*Vm*E*cos(theta1))) # A\n",
"Pr=Ior**2*R # W\n",
"print '\\n (c) Power dissipated in the resistor = %.2f W'%(Pr)\n",
"pf=(Pr+P)/Vs/Ior # power factor\n",
"print '\\n (d) Power factor = %.4f'%(pf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.5 page 122"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average load voltage = 193.2 V\n",
"\n",
" Average load current = 9.66 A\n",
"\n",
" rms load current = 11.33 A\n",
"\n",
" Average thyristor current = 4.83 A\n",
"\n",
" rms thyristor current = 8.014 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=20 # ohm\n",
"V=230 # V\n",
"f=50 # Hz\n",
"alpha=30 # degree\n",
"Vm=V*sqrt(2) # V\n",
"Vo=Vm/pi*(1+cos(alpha*pi/180)) # V\n",
"print 'Average load voltage = %.1f V'%(Vo)\n",
"Io=Vo/R # A\n",
"print '\\n Average load current = %.2f A'%( Io)\n",
"Vor=V/sqrt(pi)*sqrt((pi-alpha*pi/180)+sin(2*alpha*pi/180)/2) # V\n",
"Ior=Vor/R # A\n",
"print '\\n rms load current = %.2f A'%( Ior)\n",
"Iav=Io/2 # A\n",
"print '\\n Average thyristor current = %.2f A'%( Iav)\n",
"Irms=Ior/sqrt(2) # A\n",
"print '\\n rms thyristor current = %.3f A'%( Irms)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.6 page 122"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average load current = 4.642 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=10 # ohm\n",
"L=100/1000 # H\n",
"E=100 # V\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 45 # degree\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=2*Vm/pi*cos(alpha*pi/180) # V\n",
"Io=(Vo-E)/R # A\n",
"print 'Average load current = %.3f A'%(Io)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.7 page 123"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Average load voltage = 179.33 V\n",
"\n",
" Average load current = 89.67 A\n",
"\n",
" Power factor = 0.7797\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=2 # ohm\n",
"L=0.3 # H\n",
"E=100 # V\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 30 # degree\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=2*Vm/pi*cos(alpha*pi/180) # V\n",
"print ' Average load voltage = %.2f V'%( Vo)\n",
"Io=(Vo)/R # A\n",
"print '\\n Average load current = %.2f A'%( Io)\n",
"Is=Io # A\n",
"Is1=4*Io/pi/sqrt(2) # A\n",
"PF=Vo*Io/Vs/Is # power factor\n",
"print '\\n Power factor = %.4f'%(PF)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.8 page 123"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Average load voltage = 176.75 V\n",
"\n",
" Average load current = 33.35 A\n",
"\n",
" Power factor = 0.7685\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=5 # ohm\n",
"L=1 # H\n",
"E=10 # V\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 45 # degree\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=Vm/pi*(1+cos(alpha*pi/180)) # V\n",
"print ' Average load voltage = %.2f V'%( Vo)\n",
"Io=(Vo-E)/R # A\n",
"print '\\n Average load current = %.2f A'%( Io)\n",
"PF=(Io**2*R+E*Io)/Vs/Io # power factor\n",
"print '\\n Power factor = %.4f'%(PF)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.9 page 124"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" (i) Average voltage across 50 ohm resistor = 179.33 V\n",
"\n",
" (ii) rms current = 2.5361 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=50 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 30 # degree\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=2*Vm/pi*cos(alpha*pi/180) # V\n",
"print ' (i) Average voltage across 50 ohm resistor = %.2f V'%( Vo)\n",
"Io=(Vo)/R # A\n",
"Ior=Io/sqrt(2) # A\n",
"print '\\n (ii) rms current = %.4f A'%( Ior)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.10 page 124"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"emf on load side = 123.54 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=2 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 120 # degree\n",
"Ia=10 # A\n",
"\n",
"Vo=2*sqrt(2)*Vs*cos(alpha*pi/180)/pi\n",
"V=Ia*R-Vo # V\n",
"print 'emf on load side = %.2f V'%( V)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.11 page 125"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part(i)\n",
"\n",
" dc output voltage = 146.4 V\n",
"\n",
" Active power = 732.1 W\n",
"\n",
" Reactive power = 732.1 VAR\n",
"\n",
"\n",
" part(ii)\n",
"\n",
" dc output voltage = 176.7 V\n",
"\n",
" Active power = 1066.8 W\n",
"\n",
" Reactive power = -441.9 VAR\n",
"\n",
"\n",
" part(iii)\n",
"\n",
" Average load voltage = 88 V\n",
"\n",
" Average load current = 3.02 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"Vs=230 # V\n",
"Io=5 # A\n",
"alpha = 45 # degree\n",
"print 'part(i)'\n",
"Vo=2*sqrt(2)*Vs/pi*cos(alpha*pi/180) # V\n",
"print '\\n dc output voltage = %.1f V'%(Vo)\n",
"Pi=Vo*Io # W\n",
"print '\\n Active power = %.1f W'%(Pi)\n",
"Qi=2*sqrt(2)*Vs/pi*sin(alpha*pi/180)*Io # VAR\n",
"print '\\n Reactive power = %.1f VAR'%(Qi)\n",
"print '\\n\\n part(ii)'\n",
"R=Vo/Io # ohm\n",
"Vo=sqrt(2)*Vs/pi*(1+cos(alpha*pi/180)) # V\n",
"print '\\n dc output voltage = %.1f V'%(Vo)\n",
"Io=Vo/R # A\n",
"Pi=Vo*Io # W\n",
"print '\\n Active power = %.1f W'%(Pi)\n",
"Qi=sqrt(2)*Vs/pi*sin(alpha*pi/4)*Io # VAR\n",
"print '\\n Reactive power = %.1f VAR'%(Qi)\n",
"print '\\n\\n part(iii)'\n",
"Vo=sqrt(2)*Vs/pi/2*(1+cos(alpha*pi/180)) # \n",
"print '\\n Average load voltage = %.0f V'%(Vo)\n",
"Io=Vo/R # A\n",
"print '\\n Average load current = %.2f A'%(Io)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.12 page 126"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Average load voltage = 467.818 V\n",
"\n",
" Average load current = 23.391 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"R=20 # ohm\n",
"Vs=400 # V\n",
"f=50 # Hz\n",
"alpha = 30 # degree\n",
"\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=3*Vm/pi*cos(alpha*pi/180) # V\n",
"Io=Vo/R # A\n",
"print '\\n Average load voltage = %.3f V'%(Vo)\n",
"print '\\n Average load current = %.3f A'%(Io)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.13 page 126"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" (i)\n",
"\n",
" Output voltage = 270 V\n",
"\n",
" Output power = 27009 W\n",
"\n",
"\n",
" (ii)\n",
"\n",
" average current through thyristor = 33.33 A\n",
"\n",
" rms current through thyristor = 57.74 A\n",
"\n",
" peak current through thyristor = 100.00 A\n",
"\n",
"\n",
" (iii)\n",
"\n",
" PIV of thyristor = 565.7 V\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"n=3 # no. of phase\n",
"Vs=400 # V\n",
"f=50 # Hz\n",
"Io=100 # A\n",
"alpha = 60 # degree\n",
"\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=n*Vm/pi*cos(alpha*pi/180) # V\n",
"Po=Vo*Io # W\n",
"print ' (i)'\n",
"print '\\n Output voltage = %.0f V'%(Vo)\n",
"print '\\n Output power = %.0f W'%(Po)\n",
"print '\\n\\n (ii)'\n",
"Iav=Io*2*pi/3/2/pi # A\n",
"print '\\n average current through thyristor = %.2f A'%( Iav)\n",
"Ior=sqrt(Io**2*2*pi/3/2/pi) # A\n",
"print '\\n rms current through thyristor = %.2f A'%( Ior)\n",
"Ip=Io # A\n",
"print '\\n peak current through thyristor = %.2f A'%( Ip)\n",
"print '\\n\\n (iii)'\n",
"PIV=sqrt(2)*Vs # V\n",
"print '\\n PIV of thyristor = %.1f V'%(PIV)\n",
"# Ans in the book is not accurate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.14 page 127"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Average load voltage = 467.818 V\n",
"\n",
" Average load current = 7.8 A\n",
"\n",
" input power factor = 0.6752\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"n=3 # no. of phase\n",
"R=60 # ohm\n",
"Vs=400 # V\n",
"alpha = 30 # degree\n",
"\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=3*Vm/pi*cos(alpha*pi/180) # V\n",
"Io=Vo/R # A\n",
"P=Io**2*R # W\n",
"pf=P/sqrt(3)/Vs/Io # power factor\n",
"\n",
"print '\\n Average load voltage = %.3f V'%(Vo)\n",
"print '\\n Average load current = %.1f A'%(Io)\n",
"print '\\n input power factor = %.4f'%(pf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.15 page 127"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Average load voltage = 461.08 V\n",
"\n",
" Average load current = 9.22 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin\n",
"\n",
"n=3 # no. of phase\n",
"R=50 # ohm\n",
"Vs=400 # V\n",
"f=50 # Hz\n",
"alpha = 45 # degree\n",
"\n",
"Vm=Vs*sqrt(2) # V\n",
"Vo=3*Vm/2/pi*(1+cos(alpha*pi/180)) # V\n",
"Io=Vo/R # A\n",
"print '\\n Average load voltage = %.2f V'%(Vo)\n",
"print '\\n Average load current = %.2f A'%(Io)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 3.16 page 128"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Firing angle = 33.59 degree\n",
"\n",
" Overlap angle = 10.20 degree\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin,acos\n",
"\n",
"n=3 # no. of phase\n",
"Vs=400 # V\n",
"f=50 # Hz\n",
"Ls=5/1000 # H\n",
"Io=20 # A\n",
"Ri=1 # ohm\n",
"Vdc=400 # V\n",
"\n",
"Vo=Vdc+Io*Ri # V\n",
"# Vo=3*Vm/pi*cos(alpha*pi/180)-3*2*pi*f*Ls/pi*Io\n",
"Vm=sqrt(2)*Vs # V\n",
"alpha=acos((Vo+3*2*pi*f*Ls/pi*Io)/(3*Vm/pi))*180/pi # degree\n",
"\n",
"# Vo=3*Vm/pi*cos((alpha+mu)*pi/180)-3*2*pi*f*Ls/pi*Io\n",
"mu=acos((Vo-3*2*pi*f*Ls/pi*Io)/(3*Vm/pi))*180/pi-alpha # degree\n",
"print '\\n Firing angle = %.2f degree'%(alpha)\n",
"print '\\n Overlap angle = %.2f degree'%(mu)\n",
"# ans in the textbook is not accurate."
]
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"## Ex 3.17 page 128"
]
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" Load resistance = 36 ohm\n",
"\n",
" Source inductance = 7.3 mH\n",
"\n",
" Overlap angle = 6 degree\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,cos,sin,acos\n",
"\n",
"n=3 # no. of phase\n",
"Vs=400 # V\n",
"f=50 # Hz\n",
"alpha = pi/4 # radian\n",
"Io=10 # A\n",
"Vo=360 # V\n",
"\n",
"# Vo=n*Vs*sqrt(2)/pi/sqrt(2)-3*2*pi*f*Ls*Io/pi\n",
"Ls=(n*Vs*sqrt(2)/pi/sqrt(2)-Vo)/(3*2*pi*f)/(Io/pi)*1000 # mH\n",
"R=Vo/Io # ohm\n",
"print ' Load resistance = %.f ohm'%(R)\n",
"print '\\n Source inductance = %.1f mH'%(Ls)\n",
"# Vo = n*Vs*sqrt(2)/pi*cos(alpha+mu)+3*2*pi*f*Ls*Io/pi\n",
"mu=acos((Vo-3*2*pi*f*Ls/1000*Io/pi)/(n*Vs*sqrt(2)/pi))-alpha # radian\n",
"mu=mu*180/pi # degree\n",
"print '\\n Overlap angle = %.d degree'%(mu)"
]
}
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