(a) To determine Find the value of the variable resistance R o in the given circuit. Explanation Given data: Refer to Figure given in the textbook. The voltage source is 180 V. Calculation: The given circuit is modified as shown in Figure 1 to find the Thevenin voltage. In Figure 1, the current i ϕ = 0 A , since open circuited. Therefore, the voltage across the dependent voltage source is, 184 i ϕ = 0 V In Figure 1, apply Kirchhoff’s current law at node voltage v 1 as follows. ( v 1 16 ) + ( v 1 − 180 20 ) + ( v 1 − 180 10 ) + ( v 1 10 ) − 0.1 v Δ = 0 (1) In Figure 1, the voltage v Δ is calculated as follows, v Δ = ( 2 ) ( v 1 − 180 10 ) = 2 v 1 − 360 10 v Δ = 0.2 v 1 − 36 (2) Substitute equation (2) in equation (1) as follows, ( v 1 16 ) + ( v 1 − 180 20 ) + ( v 1 − 180 10 ) + ( v 1 10 ) − 0.1 ( 0.2 v 1 − 36 ) = 0 v 1 16 + v 1 20 − 180 20 + v 1 10 − 180 10 + v 1 10 − 0.02 v 1 + 3.6 = 0 0.0625 v 1 + 0.05 v 1 − 9 + 0.1 v 1 − 18 + 0.1 v 1 − 0.02 v 1 + 3.6 = 0 0.2925 v 1 − 23.4 = 0 Simplifying the above equation as follows, 0.2925 v 1 = 23.4 v 1 = 80 V Substitute 80 for v 1 in equation (2) to find v Δ in volts. v Δ = 0.2 ( 80 ) − 36 = 16 − 36 = − 20 V In Figure 1, the Thevenin voltage is, V Th = 180 + v Δ Substitute − 20 for v Δ in the above equation to find Thevenin voltage V Th . V Th = 180 + ( − 20 ) = 160 V The given circuit is modified as shown in Figure 2 to find the short circuit current. In Figure 2, the voltage v Δ = − 180 V , since short circuited. In Figure 2, apply Kirchhoff’s current law at node voltage v 1 and v 2 as follows. ( v 1 16 ) + ( v 1 − 180 20 ) + ( v 2 8 ) + ( v 2 10 ) − 0 (b) To determine Find the maximum power delivered to the variable resistor R o in the given circuit using PSPICE. (c) To determine Find the maximum power delivered by the 180 V voltage source to the circuit when R o = 16 Ω using PSPICE.

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 4, Problem 91P

(a)

To determine

Find the value of the variable resistance Ro in the given circuit.

(b)

To determine

Find the maximum power delivered to the variable resistor Ro in the given circuit using PSPICE.

(c)

To determine

Find the maximum power delivered by the 180 V voltage source to the circuit when Ro=16 Ω using PSPICE.

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Chapter 4, Problem 90P

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