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

Use nodal analysis to find the node voltage V_A (measured from ground).

V₁ = 15 VV₂ = 18 VR₁ = 2 ΩR₂ = 6 ΩR₃ = 2 Ω

V_A = V

2.Easy

Use nodal analysis to find the current I_R2 through R₂ in the direction of the arrow.

V₁ = 24 VV₂ = 10 VR₁ = 10 ΩR₂ = 12 ΩR₃ = 3 Ω

I_R2 = A

3.Medium

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

V₁ = 10 VI_s = 1 AR₁ = 20 ΩR₂ = 8 ΩR₃ = 6 ΩR₄ = 3 Ω

P_Is = W

4.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₁ in branch 1, flowing up into node A in the direction of the arrow.

V₁ = 9 VR₁ = 20 ΩV₂ = 15 VR₂ = 10 ΩV₃ = 24 VR₃ = 2 Ω

I₁ = A

5.Hard

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).

V₁ = 24 VI_s = 4 AV_s = 10 VR₁ = 15 ΩR₂ = 3 ΩR₃ = 8 Ω

V_A = V

6.Hard

The current source is adjusted until the node voltage at A is V_A = 3.5 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 9 VR₁ = 30 ΩR₂ = 10 ΩR₃ = 3 ΩR₄ = 2 ΩV_A = 3.5 V

I_s = A

Answer key

1. V_A = 9 V
2. I_R2 = −0.3118 A
3. P_Is = 2.971 W
4. I₁ = −0.3923 A
5. V_A = 8.286 V
6. I_s = 2.167 A

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