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​ = 3 Ω+−V1​20 VR2​6 ΩAIs​3 A

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

V1 = 20 VIs = 3 AR1 = 3 ΩR2 = 6 Ω
VA = V
2.Easy
R1​4 Ω+−V1​6 VR2​6 Ω+−V2​10 VR3​5 ΩA

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

V1 = 6 VR1 = 4 ΩV2 = 10 VR2 = 6 ΩR3 = 5 Ω
VA = V
3.Medium
R1​ = 2 ΩR3​ = 12 Ω+−V1​30 VR2​15 ΩAR4​3 ΩBIs​5 A

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

V1 = 30 VIs = 5 AR1 = 2 ΩR2 = 15 ΩR3 = 12 ΩR4 = 3 Ω
PIs = W
4.Medium
R1​ = 4 ΩR3​ = 4 ΩIR3​+−V1​6 VR2​8 ΩAR4​5 ΩBIs​2.5 A

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

V1 = 6 VIs = 2.5 AR1 = 4 ΩR2 = 8 ΩR3 = 4 ΩR4 = 5 Ω
IR3 = A
5.Hard
R1​ = 25 ΩR2​ = 30 ΩIR2​R4​ = 15 Ω+−V1​18 VR3​25 ΩAR5​15 ΩBIs​3 A+−V2​12 V

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

V1 = 18 VIs = 3 AV2 = 12 VR1 = 25 ΩR2 = 30 ΩR3 = 25 ΩR4 = 15 ΩR5 = 15 Ω
IR2 = A
6.Hard
R1​ = 15 ΩR3​ = 30 Ω+−V1​15 VR2​25 ΩAR4​15 ΩB0.2·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 node voltage VB (measured from ground).

V1 = 15 VR1 = 15 ΩR2 = 25 ΩR3 = 30 ΩR4 = 15 Ωg = 0.2 A/V
VB = V

Answer key

  1. 1. VA = 19.33 V
  2. 2. VA = 5.135 V
  3. 3. PIs = 85.26 W
  4. 4. IR3 = 1.414 A
  5. 5. IR2 = 0.51 A
  6. 6. VB = 37.5 V

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