(a) To determine Find the value of the resistor R in the given circuit. Explanation Given data: Refer to Figure given in the textbook. The voltage source is 100 V and 20 V. Calculation: In the given circuit, the Thevenin voltage is determined by removing the load resistor R between terminals a and b, and the modified circuit is shown in Figure 1. In Figure 1, apply Kirchhoff’s current law at node v 1 as follows, v 1 − 100 4 + v 1 − 20 4 + v 1 − V Th 4 = 0 v 1 − 100 + v 1 − 20 + v 1 − V Th = 0 3 v 1 − 120 − V Th = 0 3 v 1 − V Th = 120 (1) In Figure 1, apply Kirchhoff’s current law at node v 2 as follows, V Th − ( 100 + v ϕ ) 4 + V Th − v 1 4 = 0 V Th − 100 − v ϕ + V Th − v 1 = 0 2 V Th − v ϕ − v 1 = 100 (2) The dependent source constraint equation is, v ϕ = v 1 − 20 (3) Substitute equation (3) in equation (2) as follows, 2 V Th − ( v 1 − 20 ) − v 1 = 100 2 V Th − v 1 + 20 − v 1 = 100 2 V Th − 2 v 1 = 80 − v 1 + V Th = 40 (4) Adding equation (1) and (4) as follows, 2 v 1 = 160 v 1 = 80 V Substitute 80 for v 1 in equation (3) as follows, v ϕ = 80 − 20 = 60 V Substitute 80 for v 1 in equation (4) as follows, − 80 + V Th = 40 V Th = 120 V In the given circuit, the Thevenin resistance is determined by short circuiting the load resistor R between terminals a and b, and the modified circuit is shown in Figure 2. In Figure 2, apply Kirchhoff’s current law at node v 1 as follows, v 1 − 100 4 + v 1 − 20 4 + v 1 − v 2 4 = 0 v 1 − 100 + v 1 − 20 + v 1 − v 2 = 0 (5) In Figure 2, as the terminals a and b is short circuited, the node voltage v 2 is zero (b) To determine Calculate the maximum power delivered to the resistor R in the given circuit.

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 4.12, Problem 21AP

(a)

To determine

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

(b)

To determine

Calculate the maximum power delivered to the resistor R in the given circuit.

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Chapter 4.11, Problem 20AP

Chapter 4.12, Problem 22AP

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