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.

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1.Easy
R1​ = 2 ΩIR1​+−V1​6 VR2​4 ΩAIs​2 A

Use nodal analysis to find the current IR1 through R1 in the direction of the arrow.

V1 = 6 VIs = 2 AR1 = 2 ΩR2 = 4 Ω
IR1 = A
2.Easy
R1​5 Ω+−V1​15 VR2​8 Ω+−V2​12 VR3​3 ΩA

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

V1 = 15 VR1 = 5 ΩV2 = 12 VR2 = 8 ΩR3 = 3 Ω
VA = V
3.Medium
R1​ = 20 ΩR3​ = 8 Ω+−V1​30 VR2​4 ΩAR4​8 ΩBIs​1 A

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

V1 = 30 VIs = 1 AR1 = 20 ΩR2 = 4 ΩR3 = 8 ΩR4 = 8 Ω
VB = V
4.Medium
R1​ = 8 ΩR3​ = 5 Ω+−V1​12 VR2​3 ΩAR4​8 ΩBIs​2 A

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

V1 = 12 VIs = 2 AR1 = 8 ΩR2 = 3 ΩR3 = 5 ΩR4 = 8 Ω
VA = V
5.Hard
R1​ = 3 ΩR2​ = 12 ΩIR2​R4​ = 8 Ω+−V1​12 VR3​8 ΩAR5​12 ΩBIs​5 A−+V2​12 V

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 12 VIs = 5 AV2 = 12 VR1 = 3 ΩR2 = 12 ΩR3 = 8 ΩR4 = 8 ΩR5 = 12 Ω
IR2 = A
6.Hard
R1​ = 10 ΩR3​ = 4 Ω+−V1​24 VR2​8 ΩAR4​8 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 11.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 10 ΩR2 = 8 ΩR3 = 4 ΩR4 = 8 ΩVA = 11.5 V
Is = A

Answer key

  1. 1. IR1 = −0.3333 A
  2. 2. VA = 6.835 V
  3. 3. VB = 6.759 V
  4. 4. VA = 5.102 V
  5. 5. IR2 = −0.4253 A
  6. 6. Is = 1.719 A

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