(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.

Electrical Circuits and Modified MasteringEngineering - With Access

10th Edition

ISBN: 9780133992793

Author: NILSSON

Publisher: PEARSON

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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

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Electrical Circuits and Modified MasteringEngineering - With Access

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