HW3_Solution(2) (2)

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231

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Electrical Engineering

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Feb 20, 2024

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EGR231 HW3 Solutions P 4.2-2 Determine the node voltages for the circuit of Figure P 4.2-2. Answer: v 1 = 2 V, v 2 = 30 V, and v 3 = 24 V Figure P 4.2-2 Solution: KCL at node 1: KCL at node 2: KCL at node 3: Solving gives v 1 = 2 V, v 2 = 30 V and v 3 = 24 V. P4.3-4. Determine the values of the node voltages, v 1, v 2 and v 3 in the circuit shown in Figure P4.3-13. Solution: First, express the resistor currents in terms of the node voltages: Apply KCL to the supernode to get
Apply KCL at node 2 to get In matrix form: Solving using MATLAB: P4.3-14. The voltage source in the circuit shown in Figure P4.3-14 supplies 83.802 W. The current source supplies 17.572 W. Determine the values of the node voltages v 1 and v 2 . Solution: From the power supplied by the current source we calculate Using Ohm’s law From the power supplied by the voltage source we calculate Using Ohm’s law In summary v 1 = 51.905 V and v 2 = 70.288 V P 4.4-2 Find i b for the circuit shown in Figure P 4.4-2. Answer: i b = –12 mA Figure P 4.4-2 Solution: Write and solve a node equation:
P 4.4-5 Determine the value of the current i x in the circuit of Figure P 4.4-5. Answer: i x = 2.4 A Figure P 4.4-5 Solution: First, express the controlling current of the CCVS in terms of the node voltages: Next, express the controlled voltage in terms of the node voltages: so i x = 12/5 A = 2.4 A. P 4.4-11 Determine the power supplied by the dependent source in the circuit shown in Figure P 4.4-11. Figure P 4.4-11
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Solution: This circuit contains two ungrounded voltage sources, both incident to node x. In such a circuit it is necessary to merge the supernodes corresponding to the two ungrounded voltage sources into a single supernode. That single supernode separates the two voltage sources and their nodes from the rest of the circuit. It consists of the two resistors and the current source. Apply KCL to this supernode to get . The power supplied by the dependent source is .