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​8 Ω+−V2​6 VR3​12 Ω+−V3​24 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 10 VR1 = 5 ΩV2 = 6 VR2 = 8 ΩV3 = 24 VR3 = 12 Ω
VA = V
2.Easy
R1​ = 10 ΩIR1​R2​ = 6 Ω+−V1​12 VR3​12 ΩA+−V2​15 V

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

V1 = 12 VV2 = 15 VR1 = 10 ΩR2 = 6 ΩR3 = 12 Ω
IR1 = A
3.Medium
R1​ = 10 ΩR3​ = 3 ΩIR3​+−V1​30 VR2​20 ΩAR4​6 ΩBIs​5 A

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

V1 = 30 VIs = 5 AR1 = 10 ΩR2 = 20 ΩR3 = 3 ΩR4 = 6 Ω
IR3 = A
4.Medium
R1​ = 2 ΩR3​ = 5 Ω+−V1​24 VR2​6 ΩAR4​4 ΩBIs​5 A

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

V1 = 24 VIs = 5 AR1 = 2 ΩR2 = 6 ΩR3 = 5 ΩR4 = 4 Ω
VA = V
5.Hard
R1​ = 15 ΩR3​ = 20 Ω+−V1​5 VR2​5 ΩAR4​6 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 VA (measured from ground).

V1 = 5 VR1 = 15 ΩR2 = 5 ΩR3 = 20 ΩR4 = 6 Ωg = 0.05 A/V
VA = V
6.Hard
R1​ = 20 ΩR3​ = 12 Ω+−V1​15 VR2​30 ΩAR4​6 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 = 15 VR1 = 20 ΩR2 = 30 ΩR3 = 12 ΩR4 = 6 Ωg = 0.1 A/V
VA = V

Answer key

  1. 1. VA = 11.63 V
  2. 2. IR1 = 0.1429 A
  3. 3. IR3 = −0.6383 A
  4. 4. VA = 12.57 V
  5. 5. VA = 1.135 V
  6. 6. VA = 7.105 V

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