Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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**Circuit Analysis for Thévenin and Norton Equivalence** ### Given Circuit The circuit consists of: - A 9V voltage source. - A series of resistors: 12 kΩ, 36 kΩ, 12 kΩ, and 18 kΩ. These components are connected in a combination between two terminals, labeled as "a" and "b". ### Tasks a. **Find and Draw the Thévenin Equivalent Circuit** To find the Thévenin equivalent, calculate the open-circuit voltage and the equivalent resistance seen from terminals a and b when the voltage source is turned off (replacing it with a short circuit). b. **Find and Draw the Norton Equivalent Circuit** To find the Norton equivalent, determine the short-circuit current between terminals a and b and the equivalent parallel resistance (using the same method as in the Thévenin equivalent). c. **Maximum Power Transfer** For the transfer of maximum power, determine the load resistance (\(R_L\)) that should be connected across terminals a and b. According to the Maximum Power Transfer Theorem, \(R_L\) should be equal to the Thévenin resistance. d. **Calculate Maximum Power** Compute the maximum power delivered to the load resistance \(R_L\) calculated in part (c), using the formula: \[ P_{\text{max}} = \frac{V_{\text{Th}}^2}{4R_{\text{Th}}} \] where \(V_{\text{Th}}\) is the Thévenin equivalent voltage, and \(R_{\text{Th}}\) is the Thévenin equivalent resistance.
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Transcribed Image Text:**Circuit Analysis for Thévenin and Norton Equivalence** ### Given Circuit The circuit consists of: - A 9V voltage source. - A series of resistors: 12 kΩ, 36 kΩ, 12 kΩ, and 18 kΩ. These components are connected in a combination between two terminals, labeled as "a" and "b". ### Tasks a. **Find and Draw the Thévenin Equivalent Circuit** To find the Thévenin equivalent, calculate the open-circuit voltage and the equivalent resistance seen from terminals a and b when the voltage source is turned off (replacing it with a short circuit). b. **Find and Draw the Norton Equivalent Circuit** To find the Norton equivalent, determine the short-circuit current between terminals a and b and the equivalent parallel resistance (using the same method as in the Thévenin equivalent). c. **Maximum Power Transfer** For the transfer of maximum power, determine the load resistance (\(R_L\)) that should be connected across terminals a and b. According to the Maximum Power Transfer Theorem, \(R_L\) should be equal to the Thévenin resistance. d. **Calculate Maximum Power** Compute the maximum power delivered to the load resistance \(R_L\) calculated in part (c), using the formula: \[ P_{\text{max}} = \frac{V_{\text{Th}}^2}{4R_{\text{Th}}} \] where \(V_{\text{Th}}\) is the Thévenin equivalent voltage, and \(R_{\text{Th}}\) is the Thévenin equivalent resistance.
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