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​ = 12 Ω+−V1​15 VR2​6 ΩAIs​1 A

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

V1 = 15 VIs = 1 AR1 = 12 ΩR2 = 6 Ω
VA = V
2.Easy
R1​ = 5 ΩR2​ = 5 Ω+−V1​10 VR3​12 ΩIR3​A+−V2​18 V

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 10 VV2 = 18 VR1 = 5 ΩR2 = 5 ΩR3 = 12 Ω
IR3 = A
3.Medium
R1​ = 5 ΩR3​ = 6 Ω+−V1​10 VR2​10 ΩAR4​4 ΩBIs​4 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 10 VIs = 4 AR1 = 5 ΩR2 = 10 ΩR3 = 6 ΩR4 = 4 Ω
PIs = W
4.Medium
R1​15 Ω+−V1​10 VR2​6 Ω+−V2​15 VR3​15 Ω+−V3​12 VI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 10 VR1 = 15 ΩV2 = 15 VR2 = 6 ΩV3 = 12 VR3 = 15 Ω
I3 = A
5.Hard
R1​ = 8 ΩR2​ = 30 ΩR4​ = 5 Ω+−V1​15 VR3​8 ΩAR5​8 ΩBIs​1 A+−V2​5 V

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

V1 = 15 VIs = 1 AV2 = 5 VR1 = 8 ΩR2 = 30 ΩR3 = 8 ΩR4 = 5 ΩR5 = 8 Ω
VB = V
6.Hard
R1​ = 3 ΩR3​ = 12 Ω+−V1​18 VR2​3 ΩAR4​12 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 16 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 18 VR1 = 3 ΩR2 = 3 ΩR3 = 12 ΩR4 = 12 ΩVA = 16 V
Is = A

Answer key

  1. 1. VA = 9 V
  2. 2. IR3 = 0.9655 A
  3. 3. PIs = 52.8 W
  4. 4. I3 = −0.08148 A
  5. 5. VB = 6.266 V
  6. 6. Is = 10.67 A

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