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 power P_Is delivered by the current source I_s.

V₁ = 15 VI_s = 2 AR₁ = 12 ΩR₂ = 4 Ω

P_Is = W

2.Easy

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

V₁ = 8 VI_s = 3 AR₁ = 6 ΩR₂ = 6 Ω

I_R2 = A

3.Medium

Use nodal analysis to find the current I_R3 through R₃ in the direction of the arrow.

V₁ = 9 VI_s = 2.5 AR₁ = 20 ΩR₂ = 12 ΩR₃ = 20 ΩR₄ = 3 Ω

I_R3 = A

4.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 current I_x through the voltage source, from A to B as shown by the arrow.

I_s = 5 AV_s = 6 VR₁ = 12 ΩR₂ = 10 Ω

I_x = A

5.Hard

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

V₁ = 6 VI_s = 5 AV_s = 3 VR₁ = 10 ΩR₂ = 15 ΩR₃ = 8 Ω

V_B = V

6.Hard

The voltage source Vₛ between A and B has its + terminal at A, so it makes V_A − V_B = Vₛ. Use nodal analysis with a supernode to find the current I_x through the voltage source, from A to B as shown by the arrow.

V₁ = 15 VI_s = 0.5 AV_s = 4 VR₁ = 30 ΩR₂ = 25 ΩR₃ = 2 Ω

I_x = A

Answer key

1. P_Is = 19.5 W
2. I_R2 = 2.167 A
3. I_R3 = −0.1352 A
4. I_x = 3 A
5. V_B = 17.49 V
6. I_x = 0.1163 A

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