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 Ω+−V1​10 VR2​12 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 5 ΩR2 = 12 Ω
PIs = W
2.Easy
R1​ = 8 ΩIR1​+−V1​12 VR2​4 ΩAIs​1 A

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

V1 = 12 VIs = 1 AR1 = 8 ΩR2 = 4 Ω
IR1 = A
3.Medium
R1​ = 2 ΩR3​ = 8 ΩIR3​+−V1​18 VR2​6 ΩAR4​5 ΩBIs​3 A

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

V1 = 18 VIs = 3 AR1 = 2 ΩR2 = 6 ΩR3 = 8 ΩR4 = 5 Ω
IR3 = A
4.Medium
R1​ = 2 ΩR3​ = 20 Ω+−V1​15 VR2​20 ΩAR4​10 ΩBIs​2 A

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

V1 = 15 VIs = 2 AR1 = 2 ΩR2 = 20 ΩR3 = 20 ΩR4 = 10 Ω
VA = V
5.Hard
R1​ = 10 ΩR2​ = 12 ΩIR2​R4​ = 30 Ω+−V1​6 VR3​5 ΩAR5​30 ΩBIs​2 A−+V2​10 V

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

V1 = 6 VIs = 2 AV2 = 10 VR1 = 10 ΩR2 = 12 ΩR3 = 5 ΩR4 = 30 ΩR5 = 30 Ω
IR2 = A
6.Hard
R1​ = 4 ΩR3​ = 12 Ω+−V1​12 VR2​12 ΩAR4​30 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 = 4 ΩR2 = 12 ΩR3 = 12 ΩR4 = 30 Ωg = 0.25 A/V
VB = V

Answer key

  1. 1. PIs = 28.24 W
  2. 2. IR1 = 1.333 A
  3. 3. IR3 = −0.1034 A
  4. 4. VA = 14 V
  5. 5. IR2 = −0.7582 A
  6. 6. VB = 48 V

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