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 ΩR2​ = 3 ΩIR2​+−V1​20 VR3​6 ΩA+−V2​10 V

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

V1 = 20 VV2 = 10 VR1 = 8 ΩR2 = 3 ΩR3 = 6 Ω
IR2 = A
2.Easy
R1​8 Ω+−V1​15 VR2​6 Ω+−V2​18 VR3​3 Ω+−V3​15 VA

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

V1 = 15 VR1 = 8 ΩV2 = 18 VR2 = 6 ΩV3 = 15 VR3 = 3 Ω
VA = V
3.Medium
R1​ = 12 ΩR3​ = 15 ΩIR3​+−V1​18 VR2​20 ΩAR4​2 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 12 ΩR2 = 20 ΩR3 = 15 ΩR4 = 2 Ω
IR3 = A
4.Medium
R1​ = 8 ΩR3​ = 5 Ω+−V1​10 VR2​5 ΩAR4​4 ΩBIs​4 A

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

V1 = 10 VIs = 4 AR1 = 8 ΩR2 = 5 ΩR3 = 5 ΩR4 = 4 Ω
PIs = W
5.Hard
R1​ = 3 ΩR3​ = 25 Ω+−V1​15 VR2​12 ΩAR4​15 ΩB0.2·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.2·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 15 VR1 = 3 ΩR2 = 12 ΩR3 = 25 ΩR4 = 15 Ωg = 0.2 A/V
VB = V
6.Hard
R1​ = 12 ΩIR1​R2​ = 2 ΩR4​ = 10 Ω+−V1​9 VR3​15 ΩAR5​12 ΩBIs​1.5 A+−V2​36 V

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

V1 = 9 VIs = 1.5 AV2 = 36 VR1 = 12 ΩR2 = 2 ΩR3 = 15 ΩR4 = 10 ΩR5 = 12 Ω
IR1 = A

Answer key

  1. 1. IR2 = −0.2222 A
  2. 2. VA = 15.8 V
  3. 3. IR3 = 0.7857 A
  4. 4. PIs = 47.9 W
  5. 5. VB = 30.68 V
  6. 6. IR1 = −0.5644 A

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