In the circuit of Fig. 11.46, find the value of ZL that will absorb the maximum power and the value of the maximum power.
Find the value of the load impedance
Answer to Problem 15P
The value of load impedance
Explanation of Solution
Given data:
Refer to Figure 11.46 in the textbook.
The inductance
The capacitance C is
The source voltage is
Formula used:
Write the expression to find the maximum average power.
Here,
Write the general expression for load impedance
Calculation:
Refer to Figure 11.46 in the textbook.
In the circuit, to calculate the Thevenin impedance
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 (3) in equation (4) to find
Rearrange the equation as follows,
The Thevenin impedance is,
Substitute
Simplify the equation as follows,
For maximum average power transfer, the load impedance
On comparing the equation with equation (2),
The given circuit of Figure 11.46 is modified as shown in Figure 2.
In Figure 2, apply Kirchhoff’s 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
The voltage
Convert the equation from rectangular to polar form.
The Thevenin voltage,
Substitute
Conclusion:
Thus, The value of load impedance
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