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​8 Ω+−V1​18 VR2​8 Ω+−V2​8 VR3​12 ΩA

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

V1 = 18 VR1 = 8 ΩV2 = 8 VR2 = 8 ΩR3 = 12 Ω
VA = V
2.Easy
R1​ = 5 ΩR2​ = 4 ΩIR2​+−V1​8 VR3​12 ΩA+−V2​8 V

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

V1 = 8 VV2 = 8 VR1 = 5 ΩR2 = 4 ΩR3 = 12 Ω
IR2 = A
3.Medium
−+Vs​ = 9 VIx​Is​1.5 AAR1​15 ΩR2​20 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 = 1.5 AVs = 9 VR1 = 15 ΩR2 = 20 Ω
Ix = A
4.Medium
R1​ = 5 ΩR3​ = 5 ΩIR3​+−V1​12 VR2​3 ΩAR4​8 ΩBIs​1.5 A

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 12 VIs = 1.5 AR1 = 5 ΩR2 = 3 ΩR3 = 5 ΩR4 = 8 Ω
IR3 = A
5.Hard
R1​ = 2 ΩR3​ = 5 Ω+−V1​30 VR2​6 ΩAR4​8 ΩIR4​B0.5·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.5·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 = 30 VR1 = 2 ΩR2 = 6 ΩR3 = 5 ΩR4 = 8 Ωg = 0.5 A/V
IR4 = A
6.Hard
R1​ = 2 ΩR3​ = 12 Ω+−V1​5 VR2​15 ΩAR4​15 ΩIR4​B0.25·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 current IR4 through R4 in the direction of the arrow.

V1 = 5 VR1 = 2 ΩR2 = 15 ΩR3 = 12 ΩR4 = 15 Ωg = 0.25 A/V
IR4 = A

Answer key

  1. 1. VA = 9.75 V
  2. 2. IR2 = −0.3125 A
  3. 3. Ix = 0.9 A
  4. 4. IR3 = −0.5042 A
  5. 5. IR4 = 9.265 A
  6. 6. IR4 = 0.7968 A

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