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​ = 10 Ω+−V1​6 VR2​5 ΩAIs​3 A

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

V1 = 6 VIs = 3 AR1 = 10 ΩR2 = 5 Ω
PIs = W
2.Easy
R1​ = 2 Ω+−V1​12 VR2​3 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 2 ΩR2 = 3 Ω
VA = V
3.Medium
R1​6 Ω+−V1​12 VR2​8 Ω+−V2​15 VR3​6 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 = 12 VR1 = 6 ΩV2 = 15 VR2 = 8 ΩR3 = 6 Ω
I3 = A
4.Medium
−+Vs​ = 9 VIx​Is​1 AAR1​8 ΩR2​6 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 current Ix through the voltage source, from A to B as shown by the arrow.

Is = 1 AVs = 9 VR1 = 8 ΩR2 = 6 Ω
Ix = A
5.Hard
R1​ = 4 ΩR3​ = 5 Ω+−V1​6 VR2​2 ΩAR4​15 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 = 6 VR1 = 4 ΩR2 = 2 ΩR3 = 5 ΩR4 = 15 Ωg = 0.05 A/V
IR4 = A
6.Hard
R1​ = 30 ΩR3​ = 30 Ω+−V1​10 VR2​3 ΩAR4​6 ΩB0.05·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 node voltage VA (measured from ground).

V1 = 10 VR1 = 30 ΩR2 = 3 ΩR3 = 30 ΩR4 = 6 Ωg = 0.05 A/V
VA = V

Answer key

  1. 1. PIs = 36 W
  2. 2. VA = 10.8 V
  3. 3. I3 = −1.409 A
  4. 4. Ix = 1.214 A
  5. 5. IR4 = 0.123 A
  6. 6. VA = 0.8633 V

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