(a) To determine Find the value of the load resistor R L in the given circuit. Explanation Given data: Refer to Figure given in the textbook. Calculation: In the given circuit, the Thevenin resistance is determined by removing the load resistor R L and the modified circuit is shown in Figure 1. In Figure 1, apply Kirchhoff’s voltage law to loop i 1 as follows, − 3600 + 45 ( i 1 − i 2 ) + 300 ( i 1 − i 3 ) + 30 i 1 = 0 { ∵ 1 k = 10 3 } − 3600 + 45 i 1 − 45 i 2 + 300 i 1 − 300 i 3 + 30 i 1 = 0 375 i 1 − 45 i 2 − 300 i 3 = 3600 (1) In Figure 1, apply Kirchhoff’s voltage law to loop i 2 as follows, 30 i 2 + 60 ( i 2 − i 3 ) + 45 ( i 2 − i 1 ) = 0 30 i 2 + 60 i 2 − 60 i 3 + 45 i 2 − 45 i 1 = 0 − 45 i 1 + 135 i 2 − 60 i 3 = 0 (2) In Figure 1, apply Kirchhoff’s voltage law to loop i 3 as follows, − 150 i β + 15 i 3 + 300 ( i 3 − i 1 ) + 60 ( i 3 − i 2 ) = 0 − 150 i β + 15 i 3 + 300 i 3 − 300 i 1 + 60 i 3 − 60 i 2 = 0 − 150 i β − 300 i 1 − 60 i 2 + 375 i 3 = 0 (3) The dependent source constraint equation is, i β = i 1 − i 2 (4) Substitute equation (4) in equation (3) as follows, − 150 ( i 1 − i 2 ) − 300 i 1 − 60 i 2 + 375 i 3 = 0 − 150 i 1 + 150 i 2 − 300 i 1 − 60 i 2 + 375 i 3 = 0 − 450 i 1 + 90 i 2 + 375 i 3 = 0 (5) Multiply equation (1) by 2 as follows, 750 i 1 − 90 i 2 − 600 i 3 = 7200 (6) Adding equation (6) and (5) as follows, 300 i 1 − 225 i 3 = 7200 (7) Multiply equation (1) by 3 as follows, 1125 i 1 − 135 i 2 − 900 i 3 = 10800 (8) Adding equation (8) and (2) as follows, 1080 i 1 − 960 i 3 = 10800 (9) Rearranging equation (7) as follows, 300 i 1 = 7200 + 225 i 3 i 1 = 24 + 0.75 i 3 (10) Substitute equation (10) in equation (9) as follows, 1080 ( 24 + 0.75 i 3 ) − 960 i 3 = 10800 25920 + 810 i 3 − 960 i 3 = 10800 − 150 i 3 = − 15120 i 3 = 100.8 A Substitute 100.8 for i 3 in equation (10) as follows, i 1 = 24 + 0.75 ( 100.8 ) = 99.6 A Substitute 100.8 for i 3 and 99.6 for i 1 in equation (2) as follows, − 45 ( 99.6 ) + 135 i 2 − 60 ( 100.8 ) = 0 − 4482 + 135 i 2 − 6048 = 0 135 i 2 = 10530 i 2 = 78 A Substitute 78 for i 2 and 99.6 for i 1 in equation (4) as follows, i β = 99.6 − 78 = 21.6 A In Figure 1, the Thevenin voltage is, V Th = 300 ( i 1 − i 3 ) Substitute 99.6 for i 1 and 100.8 for i 3 in the above equation as follows, V Th = 300 ( 99 (b) To determine Find the maximum power transferred to the load resistor R L in the given circuit.

10th Edition

ISBN: 8220100801792

Author: Riedel

Publisher: YUZU

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Chapter 4, Problem 90P

(a)

To determine

Find the value of the load resistor $RL$ in the given circuit.

(b)

To determine

Find the maximum power transferred to the load resistor $RL$ in the given circuit.

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Chapter 4, Problem 89P

Chapter 4, Problem 91P

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Find the value of the load resistor R L in the given circuit.