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​ = 4 Ω+−V1​12 VR2​?AIs​2 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 2 AR1 = 4 ΩVA = 14.5 V
R2 = Ω
2.Easy
R1​ = 5 Ω+−V1​18 VR2​4 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 5 ΩR2 = 4 Ω
PIs = W
3.Medium
R1​12 Ω+−V1​15 VI1​R2​5 Ω−+V2​24 VR3​20 ΩA

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 = 15 VR1 = 12 ΩV2 = 24 VR2 = 5 ΩR3 = 20 Ω
I1 = A
4.Medium
−+Vs​ = 9 VIs​3 AAR1​8 ΩR2​12 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VA (measured from ground).

Is = 3 AVs = 9 VR1 = 8 ΩR2 = 12 Ω
VA = V
5.Hard
R1​ = 15 ΩIR1​R2​ = 15 ΩR4​ = 10 Ω+−V1​12 VR3​4 ΩAR5​6 ΩBIs​2 A+−V2​12 V

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

V1 = 12 VIs = 2 AV2 = 12 VR1 = 15 ΩR2 = 15 ΩR3 = 4 ΩR4 = 10 ΩR5 = 6 Ω
IR1 = A
6.Hard
R1​ = 8 ΩR3​ = 10 Ω+−V1​9 VR2​6 ΩAR4​3 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 = 9 VR1 = 8 ΩR2 = 6 ΩR3 = 10 ΩR4 = 3 Ωg = 0.4 A/V
IR4 = A

Answer key

  1. 1. R2 = 10.55 Ω
  2. 2. PIs = 44 W
  3. 3. I1 = 2.137 A
  4. 4. VA = 10.8 V
  5. 5. IR1 = 0.6847 A
  6. 6. IR4 = 1.566 A

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