TD4 Circuits Électriques ARQS – Corrigé Exercices Physique-Chimie

TD4 : Circuits électriques dans l’ARQS – Corrigé
Exercice 1  
  dc/fd    f   
      c/f'                    
Exercice 2    
          S   i=Svnq  v=i/(Snq)'×− − 
Exercice 3    
   Ai1+i4−i2= 0 ⇒i4=− 
   Bi1+i3+i4−i2= 0 ⇒i4= 
   Ci4−i1−i2−i3= 0 ⇒i4= 
   Di1+i3+i4+i2= 0 ⇒i4=− 
   Ei+i1+i3−i2= 0   Fi4−i0−i= 0  i4=i0−i1−i3+i2=, 
Exercice 4    
 U4+U1+U2= 0 ⇒U4=−  
 U4−U3+U1−U2= 0 ⇒U4=  
 U4+U1−U2= 0 ⇒U4=               U4+U3−U5= 0 ⇒
U4=   
Exercice 5     
E
i
A
R1
i1
R2
i2
E
i
A
R1
i1
i2R2R3
U
U2
E
R
2R
i2
i
20R
i1
U
4R
12R
U1
        Ai=i1+i2=E/R1+E/R2=E(1/R1+ 1/R2)
        Ai=i1+i2=E/R1+i2   i2  R2 R3 Req =R2+R3i2=
E/Req =E/(R2+R3)   i=E/R1+E/(R2+R3) = E(1/R1+1/(R2+R3))  U=R3i2=ER3/(R2+R3)
                  ⇒  
    ⇒       ⇒       ⇒  i=E/(5R)
U         2R Req = 3R  U1=E−Ri = 4E/5  U=
4E/5 ×3R/5R= 12E/25
i2=U/(12R) = E/(25R) i1=U/(4R) = 3E/(25R).
Exercice 6    
E
U
R1
R2R3
R4
U2
U1
           U1=E×
R1/(R1+R4) U2=E×R2/(R2+R3)       
  U2−U1+U= 0  U=U1−U2=E×R1
R1+R4
−R2
R2+R3
     U= 0  R1R3−R2R4= 0
Exercice 7   
 1
Req
=1
R1
+1
R2
+1
R3
 Req =R1+R2+R5(R3+R4)
R5+R3+R4
 Req =R4R3(R1+R2)
R3R4+ (R3+R4)(R1+R2)
Exercice 8    
 i=E/(R+r)
 PR=Ri2=RE2/(R+r)2
 PG=E×i=E2/(R+r)
    γ=PR/PG=R/(R+r)
 U=R×i=E×R/(R+r)
Exercice 9   
E
r
i
U
          U=E−ri  E=U+ri
         Pc=ri2        
         Pg=E×i
      γ=P
Pg
=P
Ei =P (U+ri)i=P P+ri2   i=P/U   
γ=P
P+r(P/U)2=1 1 + rP /U2
                U    
Exercice 10    
u
i
Vs
  UD< V        
i= 0   UD< Vseuil       
   E=Vs    γ 
 i=E−Vs
R+r+γUD=Vs+γi =Vs+γE−Vs R+r+γ UG=E−ri =
E−rE−Vs
R+r+γ
      UD≤Vs E =Vs    
UG=UD=E