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 ΩIR1​+−V1​24 VR2​5 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 5 ΩR2 = 5 Ω
IR1 = A
2.Easy
R1​ = 8 Ω+−V1​24 VR2​5 ΩIR2​AIs​2 A

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

V1 = 24 VIs = 2 AR1 = 8 ΩR2 = 5 Ω
IR2 = A
3.Medium
R1​3 Ω+−V1​15 VR2​15 Ω−+V2​6 VR3​20 Ω+−V3​15 VI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 3 ΩV2 = 6 VR2 = 15 ΩV3 = 15 VR3 = 20 Ω
I3 = A
4.Medium
R1​3 Ω+−V1​6 VR2​20 Ω+−V2​10 VI2​R3​10 Ω−+V3​12 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 = 6 VR1 = 3 ΩV2 = 10 VR2 = 20 ΩV3 = 12 VR3 = 10 Ω
I2 = A
5.Hard
R1​ = 25 ΩR2​ = 20 ΩR4​ = 8 Ω+−V1​5 VR3​15 ΩAR5​30 ΩBIs​6 A+−V2​15 V

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

V1 = 5 VIs = 6 AV2 = 15 VR1 = 25 ΩR2 = 20 ΩR3 = 15 ΩR4 = 8 ΩR5 = 30 Ω
VB = V
6.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​12 VR2​10 ΩAR4​20 ΩIR4​B0.2·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 current IR4 through R4 in the direction of the arrow.

V1 = 12 VR1 = 4 ΩR2 = 10 ΩR3 = 6 ΩR4 = 20 Ωg = 0.2 A/V
IR4 = A

Answer key

  1. 1. IR1 = 1.4 A
  2. 2. IR2 = 0.6154 A
  3. 3. I3 = 0.1556 A
  4. 4. I2 = 0.3655 A
  5. 5. VB = 41.27 V
  6. 6. IR4 = 1.082 A

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