Question

In circuitul din figura se cunosc: E=26 V, r=1 ohm, R1=10 Ohm, R2=5 Ohm, R3=R4=20.

Answer 1

$2. R_{3,4}=\frac{R_3R_4}{R_3+R_4}=\frac{20*20}{20+20}= 10\Omega\\R_e=R_1+R_{3,4}+R_2=10+10+5=25\Omega=>R_e=25\Omega\\I=\frac{E}{R_e+r}=\frac{26}{25+1}=1 A=>I=1 A \\I_4R_4-I_3R_3=0<=>I_4R_4=I_3R_3<=>10I_4=10I_3=>I_4=I_3\\I=I_3+I_4=>I_3=I_4=\frac{I}{2}=\frac{1}{2}=0,5 A\\E=Ir+U<=>26=1*1+U=>U=25 V\\u=Ir=1*1=1 V=>u=1 V$

$3.R_{es}=\sum\limits^n_{i=1} {R_i} (1)\\ R_1=R_2=...=R_n(2)\\(1),(2)=>R_{es}=nR\\\frac{1}{R_{ep}}=\sum\limits^n_{i=1}{\frac{1}{R_i} } (3)\\ R_1=R_2=...=R_n(4)\\(3),(4)=>\frac{1}{R_{ep}}=\frac{n}{R}=>R_{ep}=\frac{R}{n}\\ \frac{R_{es}}{R_{ep}}=\frac{nR}{\frac{R}{n} }=n^2$