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​?AIs​3 A

The node voltage at A is measured as VA = 31.5 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 3 AR1 = 10 ΩVA = 31.5 V
R2 = Ω
2.Easy
R1​ = 8 Ω+−V1​20 VR2​2 ΩAIs​3 A

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

V1 = 20 VIs = 3 AR1 = 8 ΩR2 = 2 Ω
VA = V
3.Medium
R1​ = 20 ΩR3​ = 6 ΩIR3​+−V1​6 VR2​2 ΩAR4​5 ΩBIs​2 A

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

V1 = 6 VIs = 2 AR1 = 20 ΩR2 = 2 ΩR3 = 6 ΩR4 = 5 Ω
IR3 = A
4.Medium
R1​8 Ω−+V1​18 VR2​20 Ω+−V2​9 VR3​4 Ω+−V3​30 VI3​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 = 18 VR1 = 8 ΩV2 = 9 VR2 = 20 ΩV3 = 30 VR3 = 4 Ω
I3 = A
5.Hard
R1​ = 4 ΩR2​ = 4 ΩIR2​R4​ = 5 Ω+−V1​9 VR3​10 ΩAR5​5 ΩBIs​2 A−+V2​12 V

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

V1 = 9 VIs = 2 AV2 = 12 VR1 = 4 ΩR2 = 4 ΩR3 = 10 ΩR4 = 5 ΩR5 = 5 Ω
IR2 = A
6.Hard
R1​ = 2 ΩR3​ = 2 Ω+−V1​18 VR2​30 ΩAR4​5 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 = 18 VR1 = 2 ΩR2 = 30 ΩR3 = 2 ΩR4 = 5 Ωg = 0.25 A/V
IR4 = A

Answer key

  1. 1. R2 = 70 Ω
  2. 2. VA = 8.8 V
  3. 3. IR3 = −0.7376 A
  4. 4. I3 = 4.147 A
  5. 5. IR2 = 1.863 A
  6. 6. IR4 = 3.876 A

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