To determine Calculate the voltage v in the given circuit using node-voltage method. Explanation The given circuit is redrawn with reference node and the node voltages v , v 1 and v 2 as shown in Figure 1. Apply Kirchhoff’s current law at node v 1 in Figure 1. v 1 − v 2.5 + v 1 7.5 = 4.8 v 1 2.5 − v 2.5 + v 1 7.5 = 4.8 ( 1 2.5 + 1 7.5 ) v 1 − 1 2.5 v = 4.8 0.5333 v 1 − 0.4 v = 4.8 Rearrange the equation as follows, 0.5333 v 1 = 4.8 + 0.4 v v 1 = 4.8 + 0.4 v 0.5333 v 1 = 9.0006 + 0.75 v (1) The constraint equation due to the current-controlled voltage-source (dependent source) is calculated as follows. i x = v 1 7.5 (2) The constraint equation due to the supernode is, v + i x = v 2 (3) In Figure 1, the supernode equation is, v − v 1 2.5 + v 10 + v 2 2.5 + v 2 − 12 1 = 0 v 2.5 − v 1 2.5 + v 10 + v 2 2.5 + v 2 − 12 = 0 ( 1 2.5 + 1 10 ) v − v 1 2.5 + ( 1 2.5 + 1 ) v 2 = 12 0.5 v − 0.4 v 1 + 1.4 v 2 = 12 (4) Substitute equation (2) in equation (3). v + v 1 7.5 = v 2 v = v 2 − v 1 7

ELECTRIC CIRCUITS-W/MASTERINGENGINEERING

11th Edition

ISBN: 9780134894300

Author: NILSSON

Publisher: PEARSON

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Nodal Analysis

In the analysis of any electric circuit, nodal analysis is the method of determining the potential difference or voltage between different nodes in an electric circuit. A node is a point where two or more branches connect each other. In the nodal analysi…

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