Maximum power theory in electronics

1. Sep 22, 2011

logearav

1. The problem statement, all variables and given/known data

Please see my attachment. From the circuit
Energy transferred to the load E = Ir + IR, where r is the internal resistance and R is Load Resistance. so
I = E/(r+R)

2. Relevant equations

3. The attempt at a solution
The Power W is W = I2R = E2R/(r+R)2
Upto this i understand. I can't understand the following steps
As R changes, so does W. W will be maximum when dW/dR is zero
that is d/dR(E2R/(r+R)2) = 0
My question is why W is maximum when dW/dR = 0. Why dW/dR concept is introduced here
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Attached Files:

• 97fin-fig1a.gif
File size:
986 bytes
Views:
29
Last edited by a moderator: Sep 22, 2011
2. Sep 22, 2011

Staff: Mentor

It's the basic calculus method for minimizing or maximizing a function. Take the derivative of the function with respect to the variable you wish to minimize (or maximize) with respect to, set the derivative equal to zero and solve for that variable. The resulting value(s) of the variable will either minimize or maximize the function.

3. Sep 22, 2011

logearav

Thanks gneill. But, can't this maximum theory be explained by any other concept other than calculus method. I can't understand this method.

4. Sep 22, 2011

Staff: Mentor

Well, you could graph the function with respect to r and visually see the maximum

5. Sep 23, 2011

logearav

Thanks Gneill.