Ensayo Y Ecologia Medio Ambiente
Juliethpao9528 de Agosto de 2013
1.835 Palabras (8 Páginas)871 Visitas
SOLUCION TALLER
Solución punto 1
*Obtenga los siguientes parámetros: la tensión pico a pico (Vpp), la tensión mínima (Vmin), la tensión máxima (Vmax), el valor eficaz de la tensión (Vrms), el valor medio de la tensión (VAV), el valor medio absoluto de la tensión (VAAV), el valor eficaz de la componente fundamental, la distorsión armónica total, el factor de forma y el factor de cresta de las siguientes señales de tensión:
v(t)=150 2cos(wt)
V_pp= 2V_p= 2(150√2) = 300√2 [V_pp ]
V_min=-(150√2) [v]
V_max= (150√2) [v]
V_rms= (150√2)/√2 =150 [V_rms ]
V_AV= 0 [v]
V_(AV.abs)= 1/T ∫_0^T▒|150√2 cos〖(wt)〗 | □(24&dt)
= 1/T [∫_((-Π)/2w)^(Π/2w)▒〖[150√2 cos〖(wt)〗 ] □(24&dt)〗-∫_(Π/2w)^(3Π/2w)▒〖[150√2 cos〖(wt)〗 ] □(24&dt)〗]
= 1/T [(150√2)/w ├ sin〖(wt)〗 ┤| (Π/2w)¦((-Π)/2w)-(150√2)/w ├ sin〖(wt)〗 ┤| (3Π/2w)¦(Π/2w)]
=1/T [(150√2)/w(4)]=(150√2)/2Π(4)= (150√2)/Π(2)=
= (300√2)/Π [v]
Vrms1=(150√2)/√2 =150 [V_rms ]
Vrmsh=√(150^2-150^2)=0
DATv=THDv=(Vrmsh/Vrmas1)*100=0
*F.F=V_rms/( V_(AV.abs) ) =150Π/(300√2) =Π/( 2√2) = 1.110
*F.C=V_màx/( V_rms ) = (150√2)/150 =√2 = 1.414
b) vt150√2cost
V_pp= 150√2 [V_pp ]
V_min=0[v]
V_max= 150√2 [v]
〖V_rms〗^21/T [∫_((-Π)/2w)^(Π/2w)▒〖[150√2 cos〖(wt)〗 ]^2 □(24&dt)〗+∫_(Π/2w)^(3Π/2w)▒〖[150√2 cos〖(wt)〗 ]^2 □(24&dt)〗]
( 1)/T 〖(150√2 )〗^2 [( 1t/2 ├ +sin(2wt)/4w ) ┤| (Π/2w)¦((-Π)/2w)+( 1t/2+sin(2wt)/4w ├ )┤| (3Π/2w)¦(Π/2w)]
〖V_rms〗^2( 1)/T 〖(150√2 )〗^2 [(Π/4w+Π/4w)+2Π/4w]
〖V_rms〗^2( 1)/T 〖(150√2 )〗^2 [Π/w]
〖V_rms〗^2( 1)/2 〖(150√2 )〗^2
〖 V〗_rms= (150√2)/√2 =150 [V_rms ]
V_(AV.abs)= 1/T ∫_0^T▒|150√2 cos〖(wt)〗 | □(24&dt)
= 1/T [∫_((-Π)/2w)^(Π/2w)▒〖[150√2 cos〖(wt)〗 ] □(24&dt)〗+∫_(Π/2w)^(3Π/2w)▒〖[150√2 cos〖(wt)〗 ] □(24&dt)〗]
= 1/T [(150√2)/w ├ sin〖(wt)〗 ┤| (Π/2w)¦((-Π)/2w)+(150√2)/w ├ sin〖(wt)〗 ┤| (3Π/2w)¦(Π/2w)]
=1/T [(150√2)/w(4)]=(150√2)/2Π(4)= (150√2)/Π(2)=
= (300√2)/Π [v]
〖* V〗_AV =V_(AV.abs)= (300√2)/Π [v]
Vrms1=(150√2)/√2 =150 [V_rms ]
Vrmsh=√(150^2-150^2)=0
DATv=THDv=(Vrmsh/Vrmas1)*100=0
*F.F=V_rms/( V_(AV.abs) ) =150Π/(300√2) =Π/( 2√2) = 1.110
*F.C=V_màx/( V_rms ) = (150√2)/150 =√2 = 1.414
c)
v(t)={(150√2 cos(wt) si v(t)≥0)¦( 0 si v(t)<0 )}
V_pp= 150√2 [V_pp ]
V_min=0 [v]
V_max= (150√2) [v]
〖V_rms〗^21/T [∫_((-Π)/2w)^(Π/2w)▒〖[150√2 cos〖(wt)〗 ]^2 □(24&dt)〗+∫_(Π/2w)^(3Π/2w)▒〖0□(24&dt)〗]
V_rms= (150√2)/2 =75√2 [V_rms ]
V_(AV.abs)= 1/T ∫_0^T▒|150√2 cos〖(wt)〗 | □(24&dt)
= 1/T [∫_((-Π)/2w)^(Π/2w)▒〖[150√2 cos〖(wt)〗 ] □(24&dt)〗]
= (150√2)/Π [v]
〖* V〗_AV =V_(AV.abs)= (150√2)/Π [v]
Vrms1=(150√2)/2 =75√2 [V_rms ]
Vrmsh=√(75√2^2-75√2^2)=0
DATv=THDv=(Vrmsh/Vrmas1)*100=0
*F.F=V_rms/( V_(AV.abs) ) =(75√2 Π)/(150√2) =Π/( 2) = 1.571
*F.C= V_màx/( V_rms ) = (150√2)/(75√2) =2
d)
sea v(t)={(〖 v〗_p si 0<t<T/2)¦( 〖-v〗_(p ) si T/2<t<T )}
V_pp= 2V_p [V_pp ]
V_min=-V_p [v]
V_max= V_p [v]
V_AV= 0 [v]
〖V_rms〗^21/T [∫_0^(T/2)▒〖[V_p ]^2 □(24&dt)〗+∫_(T/2)^T▒〖[V_p ]^2 □(24&dt)〗]
( 1)/T [( V_P^2 t ├ )┤| (T/2)¦0+(V_P^2 t ├ )┤| T¦(T/2)]
〖V_rms〗^2( 1)/T [V_P^2 (T/2)+V_P^2 (T/2)]
〖V_rms〗^2( 1)/T [V_P^2 T]
〖 V〗_rms= V_p [V_rms ]
Vrms1=(4Vp/√2 Π)
Vrmsh=√(V_P^2-(16V_P^2/√2 Π))=0.435Vp
DATv=THDv=(Vrmsh/Vrmas1)*100=(0.435Vp/(4Vp/√2 Π))*100=0.483164*100=48.3164
V_(AV.abs)= 1/T ∫_0^T▒|V(t)| □(24&dt)
= 1/T [∫_0^(T/2)▒〖[V_p ] □(24&dt)〗-∫_(T/2)^T▒〖[-V_p ] □(24&dt)〗]
= 1/T [├ V_p t┤| (T/2)¦0+├ V_p t┤| T¦(T/2)]
=1/T [V_p (T/2)+V_p (T/2)]=
= V_p [v]
*F.F=( V_p)/(〖 V〗_p ) =1
*F.C=( V_p)/(〖 V〗_p ) =1
e)
sea v(t)={(□((〖 V〗_p )/t_0 ) t si 0<t<t_0)¦( 0 si 〖 t〗_0<t<T )}
V_pp= V_p [V_pp ]
V_min=0 [v]
V_max= V_p [v]
〖V_rms〗^21/T [∫_0^(t_0)▒〖[□((〖 V〗_p )/t_0 ) t]^2 □(24&dt)〗+∫_(t_0)^T▒〖[0]^2 □(24&dt)〗]
( 1)/T [( □((v_p^2 )/(〖3t〗_0^2 ))t^3 ├ )┤| t_0¦0]
〖V_rms〗^2( 1)/T [( □((v_p^2 t_0 )/3) )] [V_rms ]
〖 V〗_rms=V_p/√3 (√(t_0/T) ) [V_rms ] si t_0= T entonces 〖 V〗_rms=V_p/√3 [V_rms ]
Ahora
*V_AV= V_p/2 [v]
〖* V〗_AV =V_(AV.abs)=V_p/2 [v]
Vrms1=(Vp/2√2 Π)
Vrmsh=√(V_P^2-(V_P^2/8 Π* Π)=0.698094Vp
DATv=THDv=(Vrmsh/Vrmas1)*100=0.698094Vp/(Vp/2√2 Π)=6.2031*100=620.31
*F.C=( √3 V_p)/(〖 V〗_p ) =√3
*F.F=( 2 V_p/√3)/(〖 V〗_p ) =2/√3
f)
sea v(t)={(V_p/(T/2) t- V_p si 0<t<T/2)¦( -(v_(pt-2v_(p ) ) )si T/2<t<T )}
V_pp= 2V_p [V_pp ]
V_min=-V_p [v]
V_max= V_p [v]
V_AV= 0 [v]
〖V_rms〗^21/T [∫_0^(T/2)▒〖[□((〖 2V〗_p )/T) t-V_p ]^2 □(24&dt)〗+∫_(T/2)^T▒〖[□((〖 2V〗_p )/T) t-〖2V〗_p ]^2 □(24&dt)〗]
〖V_rms〗^21/T [∫_0^(T/2)▒〖[□((〖2V〗_P^2 )/T^2 )t^2-□(( V_p)/T) t+V_P^2 ]^2 □(24&dt)〗+∫_(T/2)^T▒〖[□((〖4V〗_P^2 )/T^2 )t^2-□(( 〖8V〗_p)/T) t+〖4V〗_P^2 ]^2 □(24&dt)〗]
〖V_rms〗^2(
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