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​12 VR2​4 Ω+−V2​8 VR3​10 ΩA

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

V1 = 12 VR1 = 6 ΩV2 = 8 VR2 = 4 ΩR3 = 10 Ω
VA = V
2.Easy
R1​ = 3 ΩIR1​R2​ = 8 Ω+−V1​20 VR3​4 ΩA+−V2​6 V

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

V1 = 20 VV2 = 6 VR1 = 3 ΩR2 = 8 ΩR3 = 4 Ω
IR1 = A
3.Medium
R1​ = 10 ΩR3​ = 15 Ω+−V1​10 VR2​5 ΩAR4​6 ΩBIs​3 A

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

V1 = 10 VIs = 3 AR1 = 10 ΩR2 = 5 ΩR3 = 15 ΩR4 = 6 Ω
PIs = W
4.Medium
R1​ = 20 ΩR3​ = 15 ΩIR3​+−V1​30 VR2​20 ΩAR4​6 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 20 ΩR2 = 20 ΩR3 = 15 ΩR4 = 6 Ω
IR3 = A
5.Hard
R1​ = 25 ΩR2​ = 15 ΩIR2​R4​ = 8 Ω+−V1​24 VR3​5 ΩAR5​15 ΩBIs​0.5 A+−V2​24 V

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

V1 = 24 VIs = 0.5 AV2 = 24 VR1 = 25 ΩR2 = 15 ΩR3 = 5 ΩR4 = 8 ΩR5 = 15 Ω
IR2 = A
6.Hard
R1​ = 10 ΩR3​ = 3 Ω+−V1​10 VR2​30 ΩAR4​5 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 = 10 VR1 = 10 ΩR2 = 30 ΩR3 = 3 ΩR4 = 5 Ωg = 0.25 A/V
VB = V

Answer key

  1. 1. VA = 7.742 V
  2. 2. IR1 = 3.176 A
  3. 3. PIs = 43.15 W
  4. 4. IR3 = 0.9677 A
  5. 5. IR2 = −0.5848 A
  6. 6. VB = 10.71 V

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