Maximum Power Transfer Question

[Mrs. Kerchief]

I've posted theorem-related questions on this newsgroup that are
honest (ungraded homework problems) and don't plan to dishonor a
take-home examination that deals with all the theorems.

But a question on an examination regarding maximum power transfer,
which I answered, or attempted to answer, by thevenizing the circuit
gave a Rth with a decimal. I doubt its accuracy for that reason.
Barring the fact that this *is* a "make-believe" classroom question
employing Thevinin's Theorem, am I wrong in being concerned that my
Rth has a value with a decimal? (Don't answer if you think I'm wrong
for asking this or feel free to tell me I shouldn't be asking.)

Second, our instructor asked for the Efficiency of the circuit once we
found the value of the load. I assume, because he and the textbook
claim it, that the value of the load must equal Rth. He also asked
for the Power of the load; and, using P(out)/P(in), I arrived at an
infinitesmal difference. I employed the equations he did for
computing Efficiency--i.e., Pout/Pin, or (according to him) I^2 x
R(load)/Eth x I.

Since this is a maximum power transfer question, am I wrong in
assuming the proportion of the value of the numerator to the
denominator *must* be 2:1 to arrive at an efficiency rating of 50%?

Thanks in advance for any responses and apologies if I stated any of
this in an uninformed or crude way.

 

[Animesh Maurya]

I've posted theorem-related questions on this newsgroup that are
honest (ungraded homework problems) and don't plan to dishonor a
take-home examination that deals with all the theorems.

But a question on an examination regarding maximum power transfer,
which I answered, or attempted to answer, by thevenizing the circuit
gave a Rth with a decimal. I doubt its accuracy for that reason.
Barring the fact that this *is* a "make-believe" classroom question
employing Thevinin's Theorem, am I wrong in being concerned that my
Rth has a value with a decimal? (Don't answer if you think I'm wrong
for asking this or feel free to tell me I shouldn't be asking.)

Value of resistance can come in decimal, so don't worry about it.

Second, our instructor asked for the Efficiency of the circuit once we
found the value of the load. I assume, because he and the textbook
claim it, that the value of the load must equal Rth. He also asked
for the Power of the load; and, using P(out)/P(in), I arrived at an
infinitesmal difference. I employed the equations he did for
computing Efficiency--i.e., Pout/Pin, or (according to him) I^2 x
R(load)/Eth x I.

Its ok. You will get 50% efficiency after calculation.

Since this is a maximum power transfer question, am I wrong in
assuming the proportion of the value of the numerator to the
denominator *must* be 2:1 to arrive at an efficiency rating of 50%?

Ratio should be 1:2 to get efficiency of 50%.

Thanks in advance for any responses and apologies if I stated any of
this in an uninformed or crude way.

Animesh Maurya