Question 10.8: a) For the circuit shown in Fig. 10.20, determine the impeda...

a) We begin by determining the Thévenin equivalent with respect to the load terminals a, b. After two source transformations involving the 20 V source, the 5Ω resistor, and the 20Ω resistor, we simplify the circuit shown in Fig. 10.20 to the one shown in Fig. 10.21. Then,

= 19.2 \angle -53.13° = 11.52 – j15.36 V.

We find the Thévenin impedance by deactivating the independent source and calculating the impedance seen looking into the terminals a and b. Thus,

For maximum average power transfer, the load impedance must be the conjugate of \pmb{Z}_{Th}, so

Z_{L} = 5.76 + j1.68 \Omega.

b) We calculate the maximum average power delivered to Z_{L} from the circuit shown in Fig. 10.22, in which we replaced the original network with its Thévenin equivalent. From Fig. 10.22, the rms magnitude of the load current I is

\pmb{I}_{eff}=\frac{\frac{19.2}{\sqrt{2}}}{2\left(5.76\right)}=1.1785 A .

The average power delivered to the load is

P = I^{2}_{eff}(5.76) = 8 W.