Concept explainers
For the circuit in Fig. 11.47, find the value of ZL that will receive the maximum power from the circuit. Then calculate the power delivered to the load ZL.
Find the value of the load impedance
Answer to Problem 16P
The value of load impedance
Explanation of Solution
Given data:
Refer to Figure 11.47 in the textbook.
The inductance
The capacitance C is
The source voltage is
Formula used:
Write the general expression for the instantaneous voltage.
Write the expression to find the maximum average power.
Here,
Write the expression for
Calculation:
On comparing equation (1) and (2), the angular frequency is,
Write the expression for the reactance of the inductance.
Substitute
Write the expression for the reactance of the capacitance.
Substitute
Refer to Figure 11.47 in the textbook.
To find the Thevenin equivalent the given Figure is modified as shown in Figure 1.
In Figure 1, apply Kirchhoff’s currrent law at node voltage
Rearrange the equation as follows,
In Figure 1, apply Kirchhoff’s currrent law at node voltage
Rearrange the equation as follows,
Substitute equation (6) in equation (5).
Rearrange the equation as follows,
The voltage voltage
Convert the equation from rectangular to polar form.
The Thevenin voltage is,
In Figure 1, to calculate the Thevenin impedance
In Figure 2, apply Kirchhoff’current law at node voltage
Rearrange the equation as follows,
In Figure 2, apply Kirchhoff’current law at node voltage
Rearrange the equation as follows,
Substitute equation (7) in equation (8).
Rearrange the equation as follows,
Convert the equation from rectangular to polar form.
The Thevenin impedance
Substitute
Convert the equation from polar to rectangular form.
For maximum average power transfer, the load impedance
Convert the equation from rectangular to polar form.
On comparing the equation (9) with equation (4).
Substitute
Conclusion:
Thus, the value of load impedance
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Chapter 11 Solutions
FUNDAMENTALS OF ELECTRONIC CIRCUITS LL
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