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​20 VR2​?AIs​2 A

The node voltage at A is measured as VA = 9 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 2 AR1 = 5 ΩVA = 9 V
R2 = Ω
2.Easy
R1​ = 2 Ω+−V1​18 VR2​?AIs​2 A

The node voltage at A is measured as VA = 15.5 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 2 AR1 = 2 ΩVA = 15.5 V
R2 = Ω
3.Medium
R1​3 Ω+−V1​10 VR2​10 Ω+−V2​6 VI2​R3​6 Ω+−V3​15 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 = 10 VR1 = 3 ΩV2 = 6 VR2 = 10 ΩV3 = 15 VR3 = 6 Ω
I2 = A
4.Medium
−+Vs​ = 9 VIs​1 AAR1​15 ΩR2​3 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 VB (measured from ground).

Is = 1 AVs = 9 VR1 = 15 ΩR2 = 3 Ω
VB = V
5.Hard
R1​ = 4 ΩR3​ = 30 Ω+−V1​36 VR2​15 ΩAR4​4 ΩIR4​B0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·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 = 36 VR1 = 4 ΩR2 = 15 ΩR3 = 30 ΩR4 = 4 Ωg = 0.05 A/V
IR4 = A
6.Hard
R1​ = 3 Ω−+Vs​ = 12 VIx​+−V1​24 VR2​8 ΩAR3​4 ΩBIs​2 A

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 current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 24 VIs = 2 AVs = 12 VR1 = 3 ΩR2 = 8 ΩR3 = 4 Ω
Ix = A

Answer key

  1. 1. R2 = 2.143 Ω
  2. 2. R2 = 4.769 Ω
  3. 3. I2 = −0.4722 A
  4. 4. VB = 4 V
  5. 5. IR4 = 1.945 A
  6. 6. Ix = 3.471 A

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