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​ = 2 Ω+−V1​20 VR2​2 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 2 ΩR2 = 2 Ω
PIs = W
2.Easy
R1​8 Ω+−V1​12 VR2​2 Ω+−V2​18 VR3​2 Ω+−V3​12 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 12 VR1 = 8 ΩV2 = 18 VR2 = 2 ΩV3 = 12 VR3 = 2 Ω
VA = V
3.Medium
R1​ = 2 ΩIR1​R3​ = 15 Ω+−V1​12 VR2​4 ΩAR4​8 ΩBIs​1 A

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

V1 = 12 VIs = 1 AR1 = 2 ΩR2 = 4 ΩR3 = 15 ΩR4 = 8 Ω
IR1 = A
4.Medium
R1​ = 15 ΩR3​ = 20 Ω+−V1​9 VR2​3 ΩAR4​15 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 15 ΩR2 = 3 ΩR3 = 20 ΩR4 = 15 Ω
VA = V
5.Hard
R1​ = 10 ΩR3​ = 15 Ω+−V1​9 VR2​4 ΩAR4​3 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 = 10 ΩR2 = 4 ΩR3 = 15 ΩR4 = 3 Ωg = 0.25 A/V
VB = V
6.Hard
R1​ = 20 ΩIR1​−+Vs​ = 8 V+−V1​5 VR2​15 ΩAR3​12 ΩBIs​3 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 IR1 through R1 in the direction of the arrow.

V1 = 5 VIs = 3 AVs = 8 VR1 = 20 ΩR2 = 15 ΩR3 = 12 Ω
IR1 = A

Answer key

  1. 1. PIs = 24 W
  2. 2. VA = 14.67 V
  3. 3. IR1 = 2 A
  4. 4. VA = −1.6 V
  5. 5. VB = 1.958 V
  6. 6. IR1 = −0.3958 A

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