- #1
Baiatul122001
- 14
- 1
- Homework Statement
- Two electromotive voltage sources E1 and E2 are connected in parallel, and the internal resistors r1 and r2, and at the terminals of the circuit, a resistor R is connected. Is the efficiency of the circuit?
- Relevant Equations
- E=(E1/r1+E2/r2)/(1/r1+1/r2)=(E1r2+E2r1)/(r1+r2)
1/r=1/r1+1/r2=(r1+r2)/r1r2=>r=r1r2/(r1+r2)
I=E/(R+r)=[(E1r2+E2r1)/(r1+r2)]/[R+r1r2/(r1+r2)]=(E1r2+E2r1)/[R(r1+r2)+r1r2]
P=RI^2=R(E1r2+E2r1)^2/[R(r1+r2)+r1r2]^2
P'=EI=(E1r2+E2r1)/(r1+r2)*(E1r2+E2r1)/[R(r1+r2)+r1r2]=(E1r2+E2r1)^2/[R(r1+r2)^2+r1r2(r1+r2)]
η=P/P'={R(E1r2+E2r1)^2/[R(r1+r2)+r1r2]^2}/{(E1r2+E2r1)^2/[R(r1+r2)^2+r1r2(r1+r2)]}=R[R(r1+r2)+r1r2(r1+r2)]/[R(r1+r2)+r1r2]^2
η=R[R(r1+r2)+r1r2(r1+r2)]/[R(r1+r2)+r1r2]^2
It does not come out as the final answer
The answer in the textbook's
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