A load impedance having a constant phase angle of -36.87°is connected across the load terminals a and b in the circuit shown in Fig. 10.23. The magnitude of $Z_{L}$ is varied until the average power delivered is the most possible under the given restriction.
a) Specify $Z_{L}$ in rectangular form.
b) Calculate the average power delivered to $Z_{L}$ .

Question

A load impedance having a constant phase angle of -36.87°is connected across the load terminals a and b in the circuit shown in Fig. 10.23. The magnitude of [latex]Z_{L}[/latex] is varied until the average power delivered is the most possible under the given restriction.
a) Specify [latex]Z_{L}[/latex] in rectangular form.
b) Calculate the average power delivered to [latex]Z_{L}[/latex].

Accepted Answer

a) From Eq. 10.50, we know that the magnitude of [latex]Z_{L}[/latex]
must equal the magnitude of [latex]Z_{Th}[/latex]. Therefore

[latex]\left|Z_{L} ight| = \left|Z_{Th} ight| = \left|3000 + j4000 ight| = 5000 \Omega[/latex].

Now, as we know that the phase angle of [latex]Z_{L}[/latex] is 36.87°,we have

[latex]Z_{L} = 5000 \angle -36.87° = 4000 - j3000\Omega [/latex].

b) With [latex]Z_{L}[/latex] set equal to 4000 - j3000Ω , the load current is

[latex] I_{eff} =\frac{10}{7000 + j1000} = 1.4142 \angle -8.13° [/latex]mA,

and the average power delivered to the load is

[latex]P = \left(1.4142 imes 10^{-3} ight)^{2}\left(4000 ight) = 8 mW[/latex].

This quantity is the maximum power that can be delivered by this circuit to a load impedance whose angle is constant at -36.87°. Again, this quantity is less than the maximum power that can be delivered if there are no restrictions on [latex]Z_{L}[/latex].

Question 10.10: A load impedance having a constant phase angle of -36.87°is ...

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