When is the max power event?

Max power transfer?

  • The concept applied here is fundamentally the same problem whether I am worried about hooking up a speaker to my power amplifier or connecting up a solar cell to an electrical load. For this problem assume that Vs = 12 V and Rint = 8 ohms. Assuming we are at the conditions for max power transfer, determine The value of RL. The power absorbed by RL. The efficiency of the circuit, that is, the ratio of power absorbed by the load to power supplied by the source.

  • Answer:

    If you do the calculus on power vs resistance you will find that max power transfer occurs when Rload = Rint. I have done it once and dont want to do it again. When Rload = Rint Rl = 8 ohms Pload = ((Vs/2)^2)/Rload = 4.5W Efficiency of the circuit = 50% (Rload = Rint so Pload = Pint)

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If you want to go through the calculus: Circuit: Vpos -- Ri -- RL -- Vneg Power to the load: PL = I^2 RL Current: I = V / (Ri + RL) Power to load becomes: RL V^2 / (Ri + RL)^2 = RL V^2 (Ri+RL)^-2 To find the maximum, take the derivative of PL with respect to RL and set that equal to zero (zero slope at the top of a hill) dPL/dRL = V^2 * (Ri+RL)^-2 - 2 * V^2 * (Ri+RL)^-3 = 0 The V^2's can be divided out. And multiplying through by (Ri+RL)^2 leaves the following: (2 RL)/(Ri + RL) = 1 which is true when Ri = RL So maximum power is transferred when RL = Ri and since both resistors also see the same current, their power dissipation will be the same so only 50% of the power gets to the load. (Kinda crummy efficiency actually) But if efficiency is what you are after, then you want a RL that is quite high.

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