Chapter - Maximum Power Theorem, PPT, DC Circuits, Semester, Engineering - Electrical Engineering (EE) PDF Download

Introduction

The slides cover the following topics:

1. Maximum Power Transfer Theorem
2. Examples

Maximum Power Theorem---------------------------------Next slide

Maximum Power Transfer Theorem

Maximum Power Theorem---------------------------------Next slide

Learning Outcomes:

Upon completion of this unit the student will be able to:

Figure 1

Maximum Power Theorem---------------------------------Next slide

Maximum Power Transfer Theorem

The power delivered by a voltage source or a current source is a function of its internal resistance and also of the load resistance. Maximum power is delivered by a source to its load when the load resistance is equal to the internal resistance of the source, that is, when

  R_in = R_L

Maximum Power Theorem---------------------------------Next slide

Proof

Maximum Power Theorem---------------------------------Next slide

Proof (continued)

To find the value of R_L that maximises the expression for P_L, we first need to differentiate the expression for P_L with respect to R_L and then equate it to zero. Computing the derivative, we obtain the following expression:

Thus, to transfer maximum power to a load, the equivalent source and load resistances must be matched, that is, equal to each other.

Maximum Power Theorem---------------------------------Next slide

Proof (continued)

 

Figure 3 depicts a plot of the load power P_L divided by E² versus the ratio of RL to Rint. Note that this value is maximum when R_L = R_int.

 

Maximum Power Theorem---------------------------------Next slide

 

When the conditions of the maximum power transfer theorem are met, the total power delivered to the load is:

Maximum Power Theorem---------------------------------Next slide

Worked Example

Given the circuit in Figure 4, where:

Maximum Power Theorem---------------------------------Next slide

Maximum Power Theorem---------------------------------Next slide

Solution (continued)

From the above table and graph we can see that the Maximum Power Transfer occurs in the load when the load resistance, RL is equal in value to the source resistance, RS that is: RS = RL = 25 Ω.

Maximum Power Theorem---------------------------------Next slide

Exercise

Plot the power dissipation of the load resistance, for several values between 1 k? and 20 k?:

Maximum Power Theorem---------------------------------Next slide

Answer

Maximum Power Theorem---------------------------------Next slide

Worked Example

Suppose we were planning to use a photovoltaic panel to generate electricity and electrolyze water into hydrogen and oxygen gas:

Maximum Power Theorem---------------------------------Next slide

Answer

Experimentally determine what amount load resistance drops exactly one-half of the panel's open-circuit voltage.

Maximum Power Theorem---------------------------------Next slide

Exercises

Maximum Power Theorem---------------------------------Next slide

Maximum Power Theorem---------------------------------Next slide

Exercise

Maximum Power Theorem---------------------------------Next slide

Exercise

Maximum Power Theorem---------------------------------Next slide

Exercise

Maximum Power Theorem---------------------------------Next slide

Exercise

Maximum Power Theorem---------------------------------Next slide

Exercise

Maximum Power Theorem---------------------------------Next slide

Exercise