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​6 Ω+−V1​24 VR2​12 Ω+−V2​12 VR3​10 ΩA

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

V1 = 24 VR1 = 6 ΩV2 = 12 VR2 = 12 ΩR3 = 10 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​12 VR2​3 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 10 ΩR2 = 3 Ω
PIs = W
3.Medium
R1​ = 10 ΩR3​ = 20 Ω+−V1​10 VR2​6 ΩAR4​3 ΩBIs​1.5 A

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

V1 = 10 VIs = 1.5 AR1 = 10 ΩR2 = 6 ΩR3 = 20 ΩR4 = 3 Ω
VA = V
4.Medium
R1​5 Ω+−V1​24 VR2​12 Ω+−V2​10 VR3​5 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 = 24 VR1 = 5 ΩV2 = 10 VR2 = 12 ΩR3 = 5 Ω
I3 = A
5.Hard
R1​ = 15 ΩR3​ = 20 Ω+−V1​12 VR2​30 ΩAR4​10 ΩB0.25·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.25·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 12 VR1 = 15 ΩR2 = 30 ΩR3 = 20 ΩR4 = 10 Ωg = 0.25 A/V
VB = V
6.Hard
R1​ = 12 ΩR2​ = 10 ΩIR2​R4​ = 5 Ω+−V1​24 VR3​25 ΩAR5​4 ΩBIs​2.5 A+−V2​15 V

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

V1 = 24 VIs = 2.5 AV2 = 15 VR1 = 12 ΩR2 = 10 ΩR3 = 25 ΩR4 = 5 ΩR5 = 4 Ω
IR2 = A

Answer key

  1. 1. VA = 14.29 V
  2. 2. PIs = 29.08 W
  3. 3. VA = 3.855 V
  4. 4. I3 = −2.331 A
  5. 5. VB = 32 V
  6. 6. IR2 = 0.1965 A

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