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 = 14 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 1 AR1 = 5 ΩVA = 14 V
R2 = Ω
2.Easy
R1​ = 12 Ω+−V1​24 VR2​6 ΩIR2​AIs​1 A

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

V1 = 24 VIs = 1 AR1 = 12 ΩR2 = 6 Ω
IR2 = A
3.Medium
R1​ = 15 ΩIR1​R3​ = 12 Ω+−V1​12 VR2​12 ΩAR4​6 ΩBIs​4 A

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

V1 = 12 VIs = 4 AR1 = 15 ΩR2 = 12 ΩR3 = 12 ΩR4 = 6 Ω
IR1 = A
4.Medium
R1​6 Ω+−V1​24 VR2​2 Ω−+V2​30 VR3​4 ΩI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 24 VR1 = 6 ΩV2 = 30 VR2 = 2 ΩR3 = 4 Ω
I3 = A
5.Hard
R1​ = 5 ΩR2​ = 10 ΩR4​ = 3 Ω+−V1​15 VR3​2 ΩAR5​12 ΩBIs​0.5 A+−V2​5 V

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

V1 = 15 VIs = 0.5 AV2 = 5 VR1 = 5 ΩR2 = 10 ΩR3 = 2 ΩR4 = 3 ΩR5 = 12 Ω
VB = V
6.Hard
R1​ = 15 ΩR3​ = 25 Ω+−V1​12 VR2​4 ΩAR4​25 ΩIR4​B0.4·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.4·VA (in A, with VA in V) up into node B. Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 12 VR1 = 15 ΩR2 = 4 ΩR3 = 25 ΩR4 = 25 Ωg = 0.4 A/V
IR4 = A

Answer key

  1. 1. R2 = 23.33 Ω
  2. 2. IR2 = 2 A
  3. 3. IR1 = 0.1081 A
  4. 4. I3 = 3 A
  5. 5. VB = 5.041 V
  6. 6. IR4 = 1.288 A

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