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The controlling current is signed: i_2 = −2 A. Hence v_x = 15i_2 = −30 V. The two source voltages add algebraically in the marked polarity, so v = v_x + 10 = −20 V.
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The controlling current is signed: i_2 = −2 A. Hence v_x = 15i_2 = −30 V. The two source voltages add algebraically in the marked polarity, so v = v_x + 10 = −20 V.
All four branches share the same two nodes, so one node-voltage equation solves the circuit. Let the top-node voltage be V. Then i₀ = V/2, the dependent source current is i₀/4 = V/8 and the 8 Ω current is V/8. KCL gives V = 8 V, hence P₈Ω = V²/8 = 8 W.
C — One less than the number of nodes. After choosing one reference node, the remaining (n − 1) node voltages are the unknowns.
C — Kirchhoff's Current Law. Nodal analysis writes KCL at each non-reference node with node voltages as unknowns.
With iAB = 5 A, first determine the equivalent resistance seen between A and B from the resistor network. The network reduction gives approximately 6.842 Ω, so VAB = iAB Req ≈ 5 × 6.842 = 34.21 V.
For a connected network, the number of independent meshes is L = b - n + 1. If 4 mesh-current equations are required, 4 = b - n + 1, giving b = n + 3.
A — Super mesh. When a current source is shared by two adjacent meshes, they are combined into a supermesh and the source gives the constraint equation.