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​ = 5 ΩIR1​R2​ = 5 Ω+−V1​10 VR3​12 ΩA+−V2​8 V

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

V1 = 10 VV2 = 8 VR1 = 5 ΩR2 = 5 ΩR3 = 12 Ω
IR1 = A
2.Easy
R1​6 Ω+−V1​18 VR2​2 Ω+−V2​12 VR3​6 ΩA

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

V1 = 18 VR1 = 6 ΩV2 = 12 VR2 = 2 ΩR3 = 6 Ω
VA = V
3.Medium
−+Vs​ = 4 VIs​2.5 AAR1​15 ΩR2​12 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VB (measured from ground).

Is = 2.5 AVs = 4 VR1 = 15 ΩR2 = 12 Ω
VB = V
4.Medium
R1​ = 20 ΩR3​ = 2 ΩIR3​+−V1​10 VR2​8 ΩAR4​15 ΩBIs​1.5 A

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

V1 = 10 VIs = 1.5 AR1 = 20 ΩR2 = 8 ΩR3 = 2 ΩR4 = 15 Ω
IR3 = A
5.Hard
R1​ = 6 ΩR3​ = 5 Ω+−V1​9 VR2​4 ΩAR4​12 ΩIR4​B0.2·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.2·VA (in A, with VA in V) up into node B. Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 9 VR1 = 6 ΩR2 = 4 ΩR3 = 5 ΩR4 = 12 Ωg = 0.2 A/V
IR4 = A
6.Hard
R1​ = 30 ΩR2​ = 3 ΩIR2​R4​ = 6 Ω+−V1​36 VR3​30 ΩAR5​15 ΩBIs​2.5 A+−V2​24 V

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

V1 = 36 VIs = 2.5 AV2 = 24 VR1 = 30 ΩR2 = 3 ΩR3 = 30 ΩR4 = 6 ΩR5 = 15 Ω
IR2 = A

Answer key

  1. 1. IR1 = 0.5103 A
  2. 2. VA = 10.8 V
  3. 3. VB = 18.44 V
  4. 4. IR3 = 1.116 A
  5. 5. IR4 = 0.5279 A
  6. 6. IR2 = 0.5192 A

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