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 ΩR2​ = 3 ΩIR2​+−V1​18 VR3​8 ΩA+−V2​20 V

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

V1 = 18 VV2 = 20 VR1 = 2 ΩR2 = 3 ΩR3 = 8 Ω
IR2 = A
2.Easy
R1​ = 12 ΩIR1​+−V1​15 VR2​2 ΩAIs​1 A

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

V1 = 15 VIs = 1 AR1 = 12 ΩR2 = 2 Ω
IR1 = A
3.Medium
R1​ = 2 ΩR3​ = 3 ΩIR3​+−V1​15 VR2​20 ΩAR4​8 ΩBIs​1.5 A

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

V1 = 15 VIs = 1.5 AR1 = 2 ΩR2 = 20 ΩR3 = 3 ΩR4 = 8 Ω
IR3 = A
4.Medium
R1​ = 20 ΩR3​ = 5 Ω+−V1​15 VR2​6 ΩAR4​3 ΩBIs​3 A

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

V1 = 15 VIs = 3 AR1 = 20 ΩR2 = 6 ΩR3 = 5 ΩR4 = 3 Ω
VB = V
5.Hard
R1​ = 10 ΩR2​ = 2 ΩR4​ = 12 ΩIR4​+−V1​18 VR3​12 ΩAR5​10 ΩBIs​0.5 A+−V2​15 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 18 VIs = 0.5 AV2 = 15 VR1 = 10 ΩR2 = 2 ΩR3 = 12 ΩR4 = 12 ΩR5 = 10 Ω
IR4 = A
6.Hard
R1​ = 6 ΩR3​ = 8 Ω+−V1​15 VR2​6 ΩAR4​3 ΩB0.4·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.4·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 = 6 ΩR2 = 6 ΩR3 = 8 ΩR4 = 3 Ωg = 0.4 A/V
VB = V

Answer key

  1. 1. IR2 = −1.217 A
  2. 2. IR1 = 0.9286 A
  3. 3. IR3 = 0.1277 A
  4. 4. VB = 7.683 V
  5. 5. IR4 = −0.7074 A
  6. 6. VB = 9.087 V

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