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​ = 4 Ω+−V1​20 VR2​6 ΩIR2​AIs​1 A

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

V1 = 20 VIs = 1 AR1 = 4 ΩR2 = 6 Ω
IR2 = A
2.Easy
R1​ = 3 ΩIR1​R2​ = 5 Ω+−V1​12 VR3​5 ΩA+−V2​20 V

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

V1 = 12 VV2 = 20 VR1 = 3 ΩR2 = 5 ΩR3 = 5 Ω
IR1 = A
3.Medium
R1​5 Ω+−V1​6 VR2​15 Ω−+V2​15 VR3​4 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 = 6 VR1 = 5 ΩV2 = 15 VR2 = 15 ΩV3 = 12 VR3 = 4 Ω
I3 = A
4.Medium
R1​ = 3 ΩR3​ = 20 ΩIR3​+−V1​15 VR2​4 ΩAR4​5 ΩBIs​3 A

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

V1 = 15 VIs = 3 AR1 = 3 ΩR2 = 4 ΩR3 = 20 ΩR4 = 5 Ω
IR3 = A
5.Hard
R1​ = 10 ΩR3​ = 8 Ω+−V1​9 VR2​5 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 11 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 10 ΩR2 = 5 ΩR3 = 8 ΩR4 = 6 ΩVA = 11 V
Is = A
6.Hard
R1​ = 30 ΩR2​ = 15 ΩR4​ = 20 Ω+−V1​30 VR3​10 ΩAR5​30 ΩBIs​2.5 A−+V2​15 V

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

V1 = 30 VIs = 2.5 AV2 = 15 VR1 = 30 ΩR2 = 15 ΩR3 = 10 ΩR4 = 20 ΩR5 = 30 Ω
VA = V

Answer key

  1. 1. IR2 = 2.4 A
  2. 2. IR1 = 0.3636 A
  3. 3. I3 = 1.452 A
  4. 4. IR3 = −0.2406 A
  5. 5. Is = 7.433 A
  6. 6. VA = 10.43 V

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