Power Developed In A Resistor Given Maximum Power Transfer
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Power Developed In A Resistor Given Maximum Power Transfer

The equivalent circuit of figure 14.1 has:
VT = 35 V, RT = 600 Ω
If the conditions of maximum power transfer exist, determine
(a) The value of RL.
(b) The power developed in RL.
(c) The efficiency of the circuit.

The strings: S7P3A32 (force-push).

The math:
Pj Problem of Interest is of type force (push).

(a) Maximum power transfer theorem: to transfer maximum power to a load, the equivalent source resistance and load resistance must be matched (equal to each other).
Source voltage = VT = 35 V, source resistance = RT = 600 &ohm, load resistance = RL.
By the maximum power transfer theorem, RT = RL = 600 Ω
Proof of maximum power transfer theorem:
Power in load = PL = IL2RL
Where IL = current in load.
IL = VT/(RT + RL)
So, PL = [VT2/(RT + RL)2]RL
The value of RL that maximizes PL satisfies:
dPL/dRL = 0
dPL/dRL = [VT2(RT + RL)2 -2VT2RL(RT + RL)]/(RT + RL)4
So, (RT + RL)2 - 2RL(RT + RL) = 0
So, RL = RT.

(b) VL = [RL/(RT + RL)]VT = 35/2 = 17.5 V.
So, PL = VL2/RL = (17.5)2/600 =0.51042 watts = 510.42 mW.

(c) Circuit efficiency = (VL/VT) x 100 = (17.5/35) x 100 = 50%.

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