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 Ω+−V1​6 VR2​5 ΩAIs​1 A

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

V1 = 6 VIs = 1 AR1 = 2 ΩR2 = 5 Ω
PIs = W
2.Easy
R1​2 Ω+−V1​20 VR2​3 Ω+−V2​18 VR3​6 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 = 20 VR1 = 2 ΩV2 = 18 VR2 = 3 ΩV3 = 15 VR3 = 6 Ω
VA = V
3.Medium
R1​ = 12 ΩIR1​R3​ = 12 Ω+−V1​18 VR2​8 ΩAR4​12 ΩBIs​5 A

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

V1 = 18 VIs = 5 AR1 = 12 ΩR2 = 8 ΩR3 = 12 ΩR4 = 12 Ω
IR1 = A
4.Medium
R1​ = 4 ΩR3​ = 5 Ω+−V1​6 VR2​20 ΩAR4​8 ΩBIs​2 A

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

V1 = 6 VIs = 2 AR1 = 4 ΩR2 = 20 ΩR3 = 5 ΩR4 = 8 Ω
VB = V
5.Hard
R1​ = 25 ΩR2​ = 10 ΩR4​ = 5 ΩIR4​+−V1​9 VR3​25 ΩAR5​20 ΩBIs​2.5 A−+V2​9 V

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

V1 = 9 VIs = 2.5 AV2 = 9 VR1 = 25 ΩR2 = 10 ΩR3 = 25 ΩR4 = 5 ΩR5 = 20 Ω
IR4 = A
6.Hard
R1​ = 25 ΩR3​ = 25 Ω+−V1​9 VR2​20 ΩAR4​15 ΩB0.1·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.1·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 9 VR1 = 25 ΩR2 = 20 ΩR3 = 25 ΩR4 = 15 Ωg = 0.1 A/V
VA = V

Answer key

  1. 1. PIs = 5.714 W
  2. 2. VA = 18.5 V
  3. 3. IR1 = 0.1667 A
  4. 4. VB = 10.61 V
  5. 5. IR4 = −0.9849 A
  6. 6. VA = 4.645 V

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