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​ = 5 Ω+−V1​10 VR2​6 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 5 ΩR2 = 6 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​15 VR2​10 ΩAIs​2 A

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

V1 = 15 VIs = 2 AR1 = 6 ΩR2 = 10 Ω
VA = V
3.Medium
R1​10 Ω−+V1​10 VR2​15 Ω+−V2​6 VI2​R3​12 Ω+−V3​15 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 10 VR1 = 10 ΩV2 = 6 VR2 = 15 ΩV3 = 15 VR3 = 12 Ω
I2 = A
4.Medium
R1​ = 8 ΩR3​ = 2 ΩIR3​+−V1​6 VR2​12 ΩAR4​15 ΩBIs​1 A

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

V1 = 6 VIs = 1 AR1 = 8 ΩR2 = 12 ΩR3 = 2 ΩR4 = 15 Ω
IR3 = A
5.Hard
R1​ = 2 ΩR3​ = 8 Ω+−V1​24 VR2​5 ΩAR4​3 ΩB0.5·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 node voltage VB (measured from ground).

V1 = 24 VR1 = 2 ΩR2 = 5 ΩR3 = 8 ΩR4 = 3 Ωg = 0.5 A/V
VB = V
6.Hard
R1​ = 5 ΩR2​ = 25 ΩR4​ = 6 Ω+−V1​18 VR3​12 ΩAR5​3 ΩBIs​1 A+−V2​9 V

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

V1 = 18 VIs = 1 AV2 = 9 VR1 = 5 ΩR2 = 25 ΩR3 = 12 ΩR4 = 6 ΩR5 = 3 Ω
VB = V

Answer key

  1. 1. PIs = 21.82 W
  2. 2. VA = 16.88 V
  3. 3. I2 = 0.2267 A
  4. 4. IR3 = −0.5229 A
  5. 5. VB = 25 V
  6. 6. VB = 5.505 V

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