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​10 VR2​?AIs​3 A

The node voltage at A is measured as VA = 13 V. Use nodal analysis to find the resistance R2.

V1 = 10 VIs = 3 AR1 = 6 ΩVA = 13 V
R2 = Ω
2.Easy
R1​ = 6 Ω+−V1​20 VR2​3 ΩAIs​1 A

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

V1 = 20 VIs = 1 AR1 = 6 ΩR2 = 3 Ω
VA = V
3.Medium
R1​8 Ω+−V1​6 VR2​10 Ω+−V2​10 VI2​R3​20 Ω+−V3​24 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 6 VR1 = 8 ΩV2 = 10 VR2 = 10 ΩV3 = 24 VR3 = 20 Ω
I2 = A
4.Medium
R1​ = 5 ΩR3​ = 20 ΩIR3​+−V1​9 VR2​3 ΩAR4​20 ΩBIs​5 A

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

V1 = 9 VIs = 5 AR1 = 5 ΩR2 = 3 ΩR3 = 20 ΩR4 = 20 Ω
IR3 = A
5.Hard
R1​ = 30 ΩR3​ = 30 Ω+−V1​5 VR2​10 ΩAR4​12 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 6.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 30 ΩR2 = 10 ΩR3 = 30 ΩR4 = 12 ΩVA = 6.5 V
Is = A
6.Hard
R1​ = 8 ΩR3​ = 3 Ω+−V1​9 VR2​2 ΩAR4​20 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 = 9 VR1 = 8 ΩR2 = 2 ΩR3 = 3 ΩR4 = 20 Ωg = 0.25 A/V
VB = V

Answer key

  1. 1. R2 = 5.2 Ω
  2. 2. VA = 4.667 V
  3. 3. I2 = −0.07273 A
  4. 4. IR3 = 2.469 A
  5. 5. Is = 2.992 A
  6. 6. VB = 3.795 V

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