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​ = 12 Ω+−V1​24 VR2​8 ΩAIs​1 A

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

V1 = 24 VIs = 1 AR1 = 12 ΩR2 = 8 Ω
PIs = W
2.Easy
R1​ = 4 ΩR2​ = 5 Ω+−V1​18 VR3​3 ΩA+−V2​10 V

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

V1 = 18 VV2 = 10 VR1 = 4 ΩR2 = 5 ΩR3 = 3 Ω
VA = V
3.Medium
R1​ = 15 ΩR3​ = 4 ΩIR3​+−V1​10 VR2​4 ΩAR4​10 ΩBIs​4 A

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

V1 = 10 VIs = 4 AR1 = 15 ΩR2 = 4 ΩR3 = 4 ΩR4 = 10 Ω
IR3 = A
4.Medium
R1​8 Ω−+V1​10 VR2​10 Ω+−V2​6 VI2​R3​5 Ω+−V3​6 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 = 8 ΩV2 = 6 VR2 = 10 ΩV3 = 6 VR3 = 5 Ω
I2 = A
5.Hard
R1​ = 3 ΩR3​ = 4 Ω+−V1​15 VR2​2 ΩAR4​6 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 VA (measured from ground).

V1 = 15 VR1 = 3 ΩR2 = 2 ΩR3 = 4 ΩR4 = 6 Ωg = 0.2 A/V
VA = V
6.Hard
R1​ = 8 ΩR3​ = 15 Ω+−V1​30 VR2​10 ΩAR4​30 ΩB0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 30 VR1 = 8 ΩR2 = 10 ΩR3 = 15 ΩR4 = 30 Ωg = 0.05 A/V
VB = V

Answer key

  1. 1. PIs = 14.4 W
  2. 2. VA = 8.298 V
  3. 3. IR3 = −2.209 A
  4. 4. I2 = 0.4706 A
  5. 5. VA = 6.148 V
  6. 6. VB = 20.45 V

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