(a) To determine Find the sources which are generating power in the given circuit using mesh current method. Explanation Given data: Refer to Figure given in the textbook. The voltage source is 50 V . Calculation: The given circuit is modified as shown in Figure 1. In Figure 1, apply Kirchhoff’s Voltage law for Loop current i 1 as follows, 0 = − 50 + 6 i 1 − 4 i 2 + 9 i Δ 6 i 1 − 4 i 2 + 9 i Δ = 50 (1) In Figure 1, the constraint equation due to the dependent source is as follows. i Δ = i 2 (2) i 3 = − 1.7 v Δ (3) v Δ = 2 i 1 (4) Substitute 2 i 1 for v Δ in equation (3) as follows, i 3 = − 1.7 ( 2 i 1 ) i 3 = − 3.4 i 1 (5) Substitute i 2 for i Δ in equation (1) as follows, 6 i 1 − 4 i 2 + 9 i 2 = 50 6 i 1 + 5 i 2 = 50 6 i 1 + 5 i 2 = 50 (6) Rearrange equation (6) as follows, 5 i 2 = 50 − 6 i 1 i 2 = 50 − 6 i 1 5 (7) In Figure 2, apply Kirchhoff’s Voltage law for Loop current i 2 as follows, 0 = − 9 i Δ − 4 i 1 + 29 i 2 − 20 i 3 (8) Substitute i 2 for i Δ in equation (8) as follows, − 9 i 2 − 4 i 1 + 29 i 2 − 20 i 3 = 0 − 4 i 1 + 20 i 2 − 20 i 3 = 0 (9) Substitute 50 − 6 i 1 5 for i 2 , − 3.4 i 1 for i 3 in equation (9) as follows, − 4 i 1 + 20 ( 50 − 6 i 1 5 ) − 20 ( − 3.4 i 1 ) = 0 − 4 i 1 + 200 − 24 i 1 + 68 i 1 = 0 40 i 1 = − 200 i 1 = − 5 A Substitute − 5 for i 1 in equation (7) to find the current i 1 in amperes. i 2 = 50 − 6 ( − 5 ) 5 = 16 A Since, i Δ = i 2 . Therefore, the current is, i Δ = i 2 = 16 A Substitute − 5 for i 1 in equation (5) to find the current i 3 in amperes. i 3 = − 3.4 ( − 5 ) = 17 A Substitute − 5 for i 1 in equation (4) to find v Δ in volts. v Δ = 2 ( − 5 ) = − 10 V The voltage across the 9 i Δ dependent voltage source is, V = 9 i Δ Substitute 16 for i Δ to find the voltage across the 9 i Δ dependent voltage source in volts. V = 9 × 16 = 144 V In Figure 1, the current i a through the 4 ohms resistor is calculated as follows, i a = i 2 − i 1 Substitute 16 for i 2 and − 5 for i 1 to find the current i a through the 4 ohms resistor in amperes (b) To determine Find the total power dissipated in the circuit using PSPICE.

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 4, Problem 47P

(a)

To determine

Find the sources which are generating power in the given circuit using mesh current method.

(b)

To determine

Find the total power dissipated in the circuit using PSPICE.

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Chapter 4, Problem 46P

Chapter 4, Problem 48P

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