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​3 Ω+−V1​12 VR2​3 Ω+−V2​8 VR3​3 ΩA

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

V1 = 12 VR1 = 3 ΩV2 = 8 VR2 = 3 ΩR3 = 3 Ω
VA = V
2.Easy
R1​ = 10 ΩR2​ = 8 Ω+−V1​6 VR3​3 ΩIR3​A+−V2​20 V

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

V1 = 6 VV2 = 20 VR1 = 10 ΩR2 = 8 ΩR3 = 3 Ω
IR3 = A
3.Medium
R1​ = 15 ΩR3​ = 6 Ω+−V1​18 VR2​3 ΩAR4​3 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 15 ΩR2 = 3 ΩR3 = 6 ΩR4 = 3 Ω
VB = V
4.Medium
R1​12 Ω−+V1​24 VI1​R2​4 Ω+−V2​18 VR3​12 Ω+−V3​18 VA

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 = 24 VR1 = 12 ΩV2 = 18 VR2 = 4 ΩV3 = 18 VR3 = 12 Ω
I1 = A
5.Hard
R1​ = 4 ΩR2​ = 3 ΩR4​ = 2 ΩIR4​+−V1​10 VR3​8 ΩAR5​4 ΩBIs​5 A−+V2​10 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 10 VIs = 5 AV2 = 10 VR1 = 4 ΩR2 = 3 ΩR3 = 8 ΩR4 = 2 ΩR5 = 4 Ω
IR4 = A
6.Hard
R1​ = 2 ΩR2​ = 12 ΩR4​ = 8 Ω+−V1​30 VR3​6 ΩAR5​30 ΩBIs​5 A+−V2​30 V

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

V1 = 30 VIs = 5 AV2 = 30 VR1 = 2 ΩR2 = 12 ΩR3 = 6 ΩR4 = 8 ΩR5 = 30 Ω
VA = V

Answer key

  1. 1. VA = 6.667 V
  2. 2. IR3 = 1.851 A
  3. 3. VB = 9.652 V
  4. 4. I1 = −2.8 A
  5. 5. IR4 = 0.2381 A
  6. 6. VA = 20.2 V

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