[tex]5)Se~da:\\ \\
R_{1}=R_{2}=10\Omega\\ \\
R_{3}=40\Omega\\ \\
U=9V\\ \\
a)R=?\Omega\\ \\
b)I_{1}=?A\\ \\
c)U_{1};U_{23}=?V\\ \\
d)I_{2};I_{3}=?A\\ \\
e)Verificati\\ \\ \\[/tex]
[tex]Formule:\\ \\
a)R=R_{1}+R_{23}\\ \\ \\
\frac 1{R_{23}}=\frac 1{R_{2}}+\frac 1{R_{3}}\\ \\
\frac 1{R_{23}}=\frac {R_{2}+R_{3}}{R_{2}\times R_{3}}\\ \\
R_{23}=\frac {R_{2}\times R_{3}}{R_{2}+R_{3}}\\ \\ \\
R=R_{1}+\frac {R_{2}\times R_{3}}{R_{2}+R_{3}}\\ \\ \\[/tex]
[tex] b)I_{1}=I\\ \\ I=\frac UR\Rightarrow I_{1}=\frac UR\\ \\ \\ c)U_{1}=I_{1}\times R_{1}\\ \\ U_{23}=U-U_{1}\\ \\ \\ d)U_{2}=U_{3}=U_{23}\\ \\ \\ I_{2}=\frac {U_{23}}{R_{2}}\\ \\ I_{3}=\frac {U_{23}}{R_{3}}\\ \\ \\ [/tex]
[tex]e)Conform~legii~1:\\ \\
I_{1}=I_{2}+I_{3},~trebuie~sa~fie~adevarat.\\ \\ \\
Calcule:\\ \\
a)R=10+\frac {10\times 40}{10+40}=18\Omega \\ \\
b)I_{1}=\frac {9}{18}=0,5A\\ \\
c)U_{1}=0,5\times 10=5V\\ \\
U_{23}=9-5=4V\\ \\
d)I_{2}=\frac {4}{10}=0,4A\\ \\
I_{3}=\frac {4}{40}=0,1A\\ \\
e)0,5=0,4+0,1\Leftrightarrow 0,5=0,5(adevarat).[/tex]
[tex]6)Se~da:\\ \\
I=3A\\ \\
R_{1}=R_{2}=5\Omega\\ \\
R_{3}=30\Omega\\ \\
R_{4}=10\Omega\\ \\
a)Cum~vad~in~desen~ai~facut~correct.\\ \\
b)R=?\Omega\\ \\
c)U=?V\\ \\
d)U_{1};U_{2};U_{4};U_{3}=?V\\ \\
I_{1};I_{2};I_{4};I_{3}=?A\\ \\ \\
[/tex]
[tex]b)\frac 1R=\frac 1{R_{12}}+\frac 1{R_{34}}\\ \\ \\
R_{12}=R_{1}+R_{2}\\ \\
R_{34}=R_{3}+R_{4}\\ \\ \\
\frac 1R=\frac 1{R_{1}+R_{2}}+\frac 1{R_{3}+R_{4}}\\ \\
\frac 1R=\frac {R_{1}+R_{2}+R_{3}+R_{4}}{(R_{1}+R_{2})\times(R_{3}+R_{4})}\\ \\
R=\frac{(R_{1}+R_{2})\times(R_{3}+R_{4})}{R_{1}+R_{2}+R_{3}+R_{4}}\\ \\ \\
c)U=I\times R\\ \\[/tex]
[tex]d)U=U_{12}=U_{34}\\ \\ \\
U_{12}=I_{12}\times R_{12}\\ \\
I_{1}=I_{2}=I_{12}~si~R_{12}=R_{1}+R_{2},~deci:\\ \\
I_{1}=I_{2}=\frac U{R_{1}+R_{2}}\\ \\
U_{1}=I_{1}\times R_{1}\\ \\
U_{2}=U-U_{1}\\ \\ \\
I_{34}=I_{3}=I_{4}\\ \\
I_{34}=I-I_{12}~sau~I_{34}=I-I_{1}\\ \\
I_{3}=I_{4}=I-I_{1}\\ \\
U_{4}=I_{4}\times R_{4}\\ \\
U_{3}=I_{3}\times R_{3}\\ \\ \\[/tex]
[tex]Calcule:\\ \\
b)R=\frac{(5+5)\times(30+10)}{5+5+30+10}=8\Omega\\ \\
c)U=3\times 8=24V\\ \\
d)I_{1}=I_{2}=\frac {24}{5+5}=2,4A\\ \\
U_{1}=2,4\times 5=12V\\ \\
U_{2}=24-12=12V\\ \\
I_{3}=I_{4}=3-2,4=0,6A\\ \\
U_{4}=0,6\times 10=6V\\ \\
U_{3}=0,6\times 30=18V\\ \\
Tabelul~in~imagine.[/tex]
[tex]7)Se~da:\\ \\
a)I=400mA=0,4A\\ \\
R_{1}=15\Omega\\ \\
R_{2}=5\Omega\\ \\
I1;I2=?A\\ \\
b)I=3A\\ \\
R_{1}=15\Omega\\ \\
R_{2}=30\Omega\\ \\
R_{3}=90\Omega\\ \\
I1;I2=?A\\ \\ \\[/tex]
[tex]Formule:\\ \\
a)U=U_{1}=U_{2}\\ \\
U=I\times R\\ \\ \\
\frac 1R=\frac 1{R_{1}}+\frac 1{R_{2}}\\ \\
\frac 1R=\frac {R_{1}+R_{2}}{R_{1}\times R_{2}}\\ \\
R=\frac{R_{1}\times R_{2}}{R_{1}+R_{2}}\\ \\ \\
I_{1}=\frac {U_{1}}{R_{1}},~deci:\\ \\
I_{1}=\frac {I\times R}{R_{1}},~analogic:\\ \\
I_{1}=\frac {I\times R}{R_{2}}\\ \\ \\[/tex]
[tex]b)U_{1}=U_{2}=U_{3}=U\\ \\
U=I\times R\\ \\ \\
\frac 1R=\frac 1{R_{1}}+\frac 1{R_{2}}+\frac 1{R_{3}}\\ \\
\frac 1R=\frac {R_{1}+R_{2}}{R_{1}\times R_{2}}+\frac 1{R_{3}}\\ \\
\frac 1R=\frac {R_{1}\times R_{2}+R_{1}\times R_{3}+R_{2}\times R_{3}}{R_{1}\times R_{2} \times R_{3}}\\ \\
R=\frac{R_{1}\times R_{2} \times R_{3}}{R_{1}\times R_{2}+R_{1}\times R_{3}+R_{2}\times R_{3}}\\ \\ \\
[/tex]
[tex]I_{1}=\frac {U_{1}}{R_{1}},~astfel:\\ \\
I_{1}=\frac {I\times R}{R_{1}},~analogic:\\ \\
I_{2}=\frac {I\times R}{R_{2}},~analogic:\\ \\
I_{3}=\frac {I\times R}{R_{3}}\\ \\ \\
Calcule:\\ \\
a)R=\frac{15\times 5}{15+5}=3,75\Omega\\ \\
I_{1}=\frac {0,4\times 3,75}{15}=0,1A\\ \\
I_{1}=\frac {0,4\times 3,75}{5}=0,3A\\ \\
b)R=\frac{15\times 30 \times 90}{15\times 30+15\times 90+30\times90}=9\Omega\\ \\
I_{1}=\frac {3\times 9}{15}=1,8A\\ \\
I_{2}=\frac {3\times 9}{30}=0,9A\\ \\
I_{3}=\frac {3\times 9}{90}=0,3A[/tex]
[tex]10)Se~da:\\ \\
R_{1}=5\Omega\\ \\
R_{2}=10\Omega\\ \\
R_{3}=15\Omega\\ \\
r=2\Omega\\ \\
U_{2}=5V\\ \\
a)Sensul\\ \\
b)Borna~pozitiva\\ \\
c)U_{1};U_{3}=?V\\ \\
d)E=?V\\ \\ \\[/tex]
[tex]Formule:\\ \\
a)De~la~B~la~C\\ \\ \\
b)Stinga~de~litera~"G"~este~+\\ \\ \\
c)I_{1}=I_{2}=I_{3}\\ \\ \\
I_{2}=\frac {U_{2}}{R_{2}}\\ \\ \\
U_{1}=I_{1}\times R_{1}\Rightarrow U_{1}=\frac {U_{2}}{R_{2}} \times R_{1},~analogic:\\ \\
U_{3}=\frac {U_{2}}{R_{2}} \times R_{3}\\ \\ \\
d)E=I\times (R+r)\\ \\ \\
R=R_{1}+R_{2}+R_{3}\\ \\ \\
I=I_{2}\Rightarrow I=\frac {U_{2}}{R_{2}}\\ \\
E=\frac {U_{2}}{R_{2}}\times (R_{1}+R_{2}+R_{3}+r)\\ \\ \\[/tex]
[tex]Calcule:\\ \\
c)U_{1}=\frac {5}{10}\times5=2,5V\\ \\
U_{3}=\frac 5{10}\times15=7,5V\\ \\
d)E=\frac {5}{10}\times (5+10+15+2)=11V[/tex]
