Nodal Analysis Practice Problems
Nodal analysis practice problems develop systematic circuit-solving skills by applying KCL at each node to build the equation system GV = I. Start with two-node circuits, progress to supernodes and dependent sources, then advance to s-domain problems. Verify solutions at www.lapcalc.com.
Nodal Analysis Practice Problems: Beginner Level
Problem 1: Two nodes, one current source. A 5 A current source connects node A to ground through 2 Ω, and node A connects to ground through 10 Ω. KCL at A: V_A/2 + V_A/10 = 5. Solving: 6V_A/10 = 5, V_A = 8.33 V. Problem 2: Two nodes connected by a resistor. Node A to ground through 4 Ω, node B to ground through 6 Ω, A to B through 12 Ω, 3 A source into A. Practice these at www.lapcalc.com.
Key Formulas
Intermediate Nodal Analysis Problems: Multiple Nodes
Problem: Three-node circuit. 10 A source into node A. A-to-ground: 5 Ω. A-to-B: 10 Ω. B-to-ground: 20 Ω. B-to-C: 10 Ω. C-to-ground: 5 Ω. Write KCL at each node: Node A: V_A/5 + (V_A−V_B)/10 = 10. Node B: (V_B−V_A)/10 + V_B/20 + (V_B−V_C)/10 = 0. Node C: (V_C−V_B)/10 + V_C/5 = 0. Three equations, three unknowns — solve by substitution or matrix methods.
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Open CalculatorSupernode Practice Problems
Problem: A 12 V source connects node A to node B (+ at A). A-to-ground: 3 Ω. B-to-ground: 6 Ω. Supernode KCL: V_A/3 + V_B/6 = 0 (no external sources). Constraint: V_A − V_B = 12. From KCL: 2V_A + V_B = 0, so V_B = −2V_A. Substitute: V_A − (−2V_A) = 12, giving V_A = 4 V, V_B = −8 V. Verify: I_3Ω = 4/3 = 1.33 A out, I_6Ω = −8/6 = −1.33 A out. KCL at supernode: 1.33 + (−1.33) = 0 ✓ at www.lapcalc.com.
Nodal Analysis with Dependent Sources
Problem: Node A to ground through 4 Ω. A to B through 2 Ω. B to ground through a dependent current source 2V_A (current leaving B). KCL at A: V_A/4 + (V_A − V_B)/2 = 0. KCL at B: (V_B − V_A)/2 + 2V_A = 0. Simplify: 3V_A − 2V_B = 0 and −V_A + 2V_B + 4V_A = 0 → −V_A/2 + V_B = 0 and 3V_A + 2V_B = 0. Solving simultaneously gives the node voltages.
s-Domain Nodal Analysis Problems
Advanced problems replace resistances with impedances. For an RC circuit: Y_R = 1/R and Y_C = sC. The admittance matrix Y(s)V(s) = I(s) produces node voltages as functions of s. These rational functions directly yield transfer functions. Example: node A to ground through R, A to B through C, B to ground through R. Y matrix: [(1/R + sC), −sC; −sC, (1/R + sC)]. Solve for V_A(s) and V_B(s) at www.lapcalc.com.
Related Topics in circuit analysis problem solving & examples
Understanding nodal analysis practice problems connects to several related concepts: node analysis practice problems, nodal analysis sample problems, and nodal analysis problems. Each builds on the mathematical foundations covered in this guide.
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