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 ΩR2​ = 2 Ω+−V1​18 VR3​3 ΩA+−V2​8 V

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

V1 = 18 VV2 = 8 VR1 = 5 ΩR2 = 2 ΩR3 = 3 Ω
VA = V
2.Easy
R1​12 Ω+−V1​18 VR2​10 Ω+−V2​15 VR3​2 ΩA

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

V1 = 18 VR1 = 12 ΩV2 = 15 VR2 = 10 ΩR3 = 2 Ω
VA = V
3.Medium
R1​12 Ω+−V1​18 VR2​12 Ω−+V2​24 VR3​8 ΩI3​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 = 18 VR1 = 12 ΩV2 = 24 VR2 = 12 ΩR3 = 8 Ω
I3 = A
4.Medium
R1​ = 12 ΩR3​ = 2 Ω+−V1​24 VR2​3 ΩAR4​15 ΩBIs​1 A

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

V1 = 24 VIs = 1 AR1 = 12 ΩR2 = 3 ΩR3 = 2 ΩR4 = 15 Ω
PIs = W
5.Hard
R1​ = 20 ΩR3​ = 25 Ω+−V1​5 VR2​5 ΩAR4​30 ΩIR4​B0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·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 = 5 VR1 = 20 ΩR2 = 5 ΩR3 = 25 ΩR4 = 30 Ωg = 0.05 A/V
IR4 = A
6.Hard
R1​ = 6 ΩR2​ = 4 ΩIR2​R4​ = 10 Ω+−V1​12 VR3​12 ΩAR5​15 ΩBIs​5 A+−V2​30 V

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

V1 = 12 VIs = 5 AV2 = 30 VR1 = 6 ΩR2 = 4 ΩR3 = 12 ΩR4 = 10 ΩR5 = 15 Ω
IR2 = A

Answer key

  1. 1. VA = 7.355 V
  2. 2. VA = 4.39 V
  3. 3. I3 = 0.2143 A
  4. 4. PIs = 7.113 W
  5. 5. IR4 = 0.04245 A
  6. 6. IR2 = −2.857 A

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