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 Ω+−V1​10 VR2​10 Ω+−V2​8 VR3​4 Ω+−V3​24 VA

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

V1 = 10 VR1 = 2 ΩV2 = 8 VR2 = 10 ΩV3 = 24 VR3 = 4 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​6 VR2​?AIs​2 A

The node voltage at A is measured as VA = 8.5 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 2 AR1 = 10 ΩVA = 8.5 V
R2 = Ω
3.Medium
R1​ = 3 ΩR3​ = 8 ΩIR3​+−V1​30 VR2​10 ΩAR4​8 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 3 ΩR2 = 10 ΩR3 = 8 ΩR4 = 8 Ω
IR3 = A
4.Medium
R1​ = 10 ΩR3​ = 2 Ω+−V1​6 VR2​10 ΩAR4​15 ΩBIs​1 A

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

V1 = 6 VIs = 1 AR1 = 10 ΩR2 = 10 ΩR3 = 2 ΩR4 = 15 Ω
VB = V
5.Hard
R1​ = 2 ΩR3​ = 6 Ω+−V1​10 VR2​2 ΩAR4​30 ΩB0.5·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.5·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 10 VR1 = 2 ΩR2 = 2 ΩR3 = 6 ΩR4 = 30 Ωg = 0.5 A/V
VB = V
6.Hard
R1​ = 15 ΩIR1​R2​ = 30 ΩR4​ = 5 Ω+−V1​24 VR3​12 ΩAR5​5 ΩBIs​4 A−+V2​15 V

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

V1 = 24 VIs = 4 AV2 = 15 VR1 = 15 ΩR2 = 30 ΩR3 = 12 ΩR4 = 5 ΩR5 = 5 Ω
IR1 = A

Answer key

  1. 1. VA = 13.88 V
  2. 2. R2 = 4.857 Ω
  3. 3. IR3 = 2.353 A
  4. 4. VB = 6.818 V
  5. 5. VB = 27.27 V
  6. 6. IR1 = 1.209 A

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