Question

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Answer 1

η1=R1/(R1+r)<=>1/3=R1/(R1+2)<=>3R1=R1+2<=>2R1=2=>R1=2/2=1 Ω

P1=R1I1²

P2=R2I2²

P1=P2=>R1I1²=R2I2²

I1=E/(R1+r)

I2=E/(R2+r)

R1E²/(R1+r)²=R2E²/(R2+r)²<=>1/3²=R2/(R2+2)²<=>9R2=R2²+4+4R2<=>R2²-5R2+4=0

Δ=25-16=9

R2'=(5-3)/2<0 N.C.

R2=(5+3)/2=8/2=4 Ω

η2=R2/(R2+r)=4/(4+2)=4/6=2/3