Mesh and Node Equations: More Circuits Containing Dependent
Sources
Introduction
The circuits in this set of problems each contain a single dependent source. These circuits can be
analyzed using mesh equation or using node equations.
When doing so, it is useful to express
the controlling current or voltage of the dependent source as a function of the mesh currents or
node voltages.
Node equations are discussed in Sections 4.3, 4.4 and 4.5 of
Introduction to Electric Circuits
by
R.C. Dorf and J.A Svoboda. Section 4.5 considers circuits that contain dependent sources. Mesh
equations are discussed in Sections 4.6 and 4.7. Section 4.7 considers circuits that contain
dependent sources.
Worked Examples
Example 1:
Consider the circuit shown in Figure 1. Find the value of the gain,
A,
of the VCVS.
Figure 1
The circuit considered in Example 1.
Solution:
Figure 2 shows the circuit from Figure 1 after replacing the voltmeter by an equivalent
open circuit and labeling the voltage measured by the voltmeter. We will analyze this circuit by
writing and solving node equations. Figure 3 shows the circuit after selecting a reference node
and numbering the other nodes. Let
v
1
,
v
2
and
v
3
denote the node voltages at nodes 1, 2 and 3,
respectively.
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Figure 2
The circuit from Figure 1 after replacing the voltmeter by an open circuit.
Figure 3
The circuit from Figure 2 after labeling the nodes.
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 Spring '08
 JUANG
 Thévenin's theorem, Voltage drop, Mains electricity

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