Question

VA ROG MULT URGENT AM NEVOIE

Answer 1

R1=R-x R2=R  R3=R+x

Rs=12Ω

Rp=12/11Ω

Rs=R1+R2+R3=R-x+R+R+x=3R

Rs=12Ω

=>3R=12=>R=4Ω=>R2=4Ω

1/Rp=1/R1+1/R2+1/R3

1/Rp-1/R2=1/R1+1/R3

11/12-1/4=1/R1+1/R3

8/12=1/R1+1/R3

2/3=1/R1+1/R2

3/2=(R1*R2)/R1+R2

1,5=[(R-x)(R+x)]/2R

$1,5*2R=R^2-x^2\\1,5*8=16-x^2\\12=16-x^2\\x^2=4\\x=+-2$

pentru x=2 => R1=2Ω; R3=6Ω

pentru x=-2 =>R1=6Ω; R3=2Ω

2.

R1=3Ω

R2=6Ω

E=30V

r=1Ω

a)pentru rezistoarele în serie(Is)

Rs=R1+R2=3+6=9Ω

E=IsRs+Is1r

=>Is=$\frac{E}{Rs+r}$=$\frac{30}{10}=3A$

pentru rezistoarele în paralel (Ip)

1/Rp=1/R1+1/R2

Rp=$\frac{R1*R2}{R1+R2}$=$\frac{6*3}{6+3}=18/9=2$Ω

=>Ip=$\frac{E}{Rp+r}$=$\frac{30}{3} =10A$

b)Us=Is*Rs=3*9=27V

Up=Ip*Rp=2*10=20V

c)U1=IsR1=3*3=9V

U2=IsR2=3*6=18V

U1=IpR1=10*3=30V

U2=IpR2=10*6=60V

d)E=I1R1-I1r

I1=E/(R1-r)=30/2=15A

E=I2R2-I2r

I2=E/(R2-r)=30/5=6A