Nodal analysis worksheet with answers

Free printable Nodal analysis worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage V_A.

V₁ = 18 VR₁ = 10 ΩV₂ = 8 VR₂ = 8 ΩR₃ = 6 Ω

V_A = V

2.Easy

Use nodal analysis to find the power P_Is delivered by the current source I_s.

V₁ = 12 VI_s = 1 AR₁ = 3 ΩR₂ = 3 Ω

P_Is = W

3.Medium

The voltage source Vₛ between A and B has its + terminal at B, so it makes V_B − V_A = Vₛ. Use nodal analysis with a supernode to find the node voltage V_A (measured from ground).

I_s = 2.5 AV_s = 12 VR₁ = 4 ΩR₂ = 3 Ω

V_A = V

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₂ in branch 2, flowing up into node A in the direction of the arrow.

V₁ = 12 VR₁ = 15 ΩV₂ = 10 VR₂ = 3 ΩR₃ = 3 Ω

I₂ = A

5.Hard

Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 24 VI_s = 5 AV₂ = 6 VR₁ = 5 ΩR₂ = 10 ΩR₃ = 30 ΩR₄ = 12 ΩR₅ = 8 Ω

I_R4 = A

6.Hard

The diamond is a voltage-controlled current source that pushes a current of 0.05·V_A (in A, with V_A in V) up into node B. Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 12 VR₁ = 20 ΩR₂ = 3 ΩR₃ = 6 ΩR₄ = 2 Ωg = 0.05 A/V

I_R4 = A

Answer key

1. V_A = 7.149 V
2. P_Is = 7.5 W
3. V_A = −2.571 V
4. I₂ = 1.455 A
5. I_R4 = −0.7156 A
6. I_R4 = 0.1966 A

Full step-by-step solutions: practise this topic on examproblems.com.