Maximum Power transfer theorem ( Power dissipation in resistors in circuits)

[girlzrule786]

the equation P = (E²R) / [(R-r)² + 4Rr]

We say that when R=r , P = E²/4R which is said to be maximum..

But if I say R→∞ , then r→0 and then P = E²/R which is greater..
So, shouldn't power be maximum for max R ?

 

[technician]

E^2/R would be zero when R = Infinity.
In electrical circuits a good way to get a feel for maximum power transfer is to think about what happens
1) When R = 0, there will be a current flowing through R but the voltage across R will be 0
therefore no power is dissipated in R
2) When R = infinity there will be a voltage across R but there will be no current therefore no power is dissipated in R
If there is no power when R =0 and no power when R = infinity the maximum power must be when R is between 0 and infinity.
Max power transfer occurs when R =r

 

[girlzrule786]

@technician ...
thank you for your time..
reading your reply, a question came in my mind... resistances absorb energy... If no current flows through a resistor, that means no energy absorbed and as you said, no power dissipated... I have learned that electrons lose their potential energy as they pass through a resistor and that PE drop across a resistor is called Voltage... If no current flows through a resistor, then why do we say that there is still a voltage across it?? In simple terms, V=IR , if I=0 then V=0 right??

This thought brings me to another confusion... when we talk about voltmeters and internal resistances, we have a formula: E = V + Ir
we say that in the case when only a voltmeter is connected across a battery, the voltmeter reading = EMF because voltmeter has infinite resistance and I=0 , putting this value in the formula gives E=V ... why don't we consider zero current passing through the voltmeter?? If we do consider it, then V=0?? I am soo confused...
It makes me believe that we mould our values and formulas to fit the result we get through experimentation even if it doesn't make sense...

 

[epenguin]

As resistance of the voltmeter is very high E=V will be a good approximation, usually as good as you need.

Get used to in Science things that are not really zero but it is useful and simplifying to consider them so.

The current is not really zero and paradoxically the voltmeter depends on it not being zero - the voltmeter is really an ammeter responding to a small current and calibrated to read volts via the theory you have been through.

 

[technician]

If the resistance is INFINITE then no current flows through it but there can still be a voltage applied to it.
The best everyday example of this is to look at a battery sitting on the table with NOTHING connected to the terminals. There is only air between the terminals and I hope that you are happy to say that this is infinite resistance (it is as near as you can get in every day experience!). There is no current flowing from the battery through the air so no power is being dissipated and the battery does not run down.
I hope this helps, I do appreciate your confusion in this, it is tricky getting to grips with some of these ideas...