Problem 52-4    Source:   Problem 10.34 - page 255 -    NILSSON, James W. & RIEDEL, Susan -    Book: Circuitos Elétricos - 5ª edição - Editora LTC - 1999.

In the circuit shown in the Figure 52-04, the R resistor is set so that the dissipating power be as large as possible. The value of the voltage source is rms. Determine:

a)   the value of R.

b)   the power dissipated by R under the conditions of item a.

Solution of the Problem 52-4   

Item a   

Calculating the Thévenin equivalent for the terminals a-b. To do this, the voltage source is short-circuited and the impedance seen from the terminals a-b is calculate. Thus, the RC series circuit is in parallel with the inductor j20 and this set in series with 20 + j60. Then:

In order to determine the voltage source of Thévenin, we must calculate the open circuit voltage at the terminals a-b. Logo:

By the maximum power transfer theorem, we known that for R to dissipate the maximum power, its value must be equal to the module of the impedance of Thévenin. Assim:

Item b   

In order to calculate the power dissipated in R in conditions of the item a, we must calculate the current that flows through the load. Knowing V_th, Z_th and R, we have:

Therefore, the power dissipated in R will be: