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​12 VR2​?AIs​1 A

The node voltage at A is measured as VA = 12.5 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 1 AR1 = 5 ΩVA = 12.5 V
R2 = Ω
2.Easy
R1​ = 2 ΩIR1​R2​ = 12 Ω+−V1​18 VR3​12 ΩA+−V2​18 V

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

V1 = 18 VV2 = 18 VR1 = 2 ΩR2 = 12 ΩR3 = 12 Ω
IR1 = A
3.Medium
R1​4 Ω+−V1​10 VI1​R2​8 Ω+−V2​10 VR3​6 Ω+−V3​15 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 10 VR1 = 4 ΩV2 = 10 VR2 = 8 ΩV3 = 15 VR3 = 6 Ω
I1 = A
4.Medium
R1​ = 8 ΩR3​ = 8 Ω+−V1​6 VR2​6 ΩAR4​3 ΩBIs​2.5 A

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

V1 = 6 VIs = 2.5 AR1 = 8 ΩR2 = 6 ΩR3 = 8 ΩR4 = 3 Ω
VA = V
5.Hard
R1​ = 3 ΩR3​ = 6 Ω+−V1​12 VR2​25 ΩAR4​8 ΩB0.5·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.5·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 = 3 ΩR2 = 25 ΩR3 = 6 ΩR4 = 8 Ωg = 0.5 A/V
VB = V
6.Hard
R1​ = 2 ΩR2​ = 25 ΩR4​ = 2 Ω+−V1​15 VR3​2 ΩAR5​3 ΩBIs​1.5 A+−V2​10 V

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

V1 = 15 VIs = 1.5 AV2 = 10 VR1 = 2 ΩR2 = 25 ΩR3 = 2 ΩR4 = 2 ΩR5 = 3 Ω
VB = V

Answer key

  1. 1. R2 = 13.89 Ω
  2. 2. IR1 = 1.125 A
  3. 3. I1 = −0.3846 A
  4. 4. VA = 0.1782 V
  5. 5. VB = 57.49 V
  6. 6. VB = 7.787 V

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