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 ΩIR1​+−V1​12 VR2​8 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 12 ΩR2 = 8 Ω
IR1 = A
2.Easy
R1​ = 12 ΩR2​ = 3 ΩIR2​+−V1​18 VR3​10 ΩA+−V2​20 V

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

V1 = 18 VV2 = 20 VR1 = 12 ΩR2 = 3 ΩR3 = 10 Ω
IR2 = A
3.Medium
−+Vs​ = 9 VIx​Is​3 AAR1​10 ΩR2​5 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the current Ix through the voltage source, from A to B as shown by the arrow.

Is = 3 AVs = 9 VR1 = 10 ΩR2 = 5 Ω
Ix = A
4.Medium
R1​ = 20 ΩR3​ = 3 Ω+−V1​10 VR2​6 ΩAR4​8 ΩBIs​4 A

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

V1 = 10 VIs = 4 AR1 = 20 ΩR2 = 6 ΩR3 = 3 ΩR4 = 8 Ω
VA = V
5.Hard
R1​ = 10 ΩR2​ = 5 ΩR4​ = 25 Ω+−V1​18 VR3​3 ΩAR5​30 ΩBIs​2.5 A+−V2​18 V

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

V1 = 18 VIs = 2.5 AV2 = 18 VR1 = 10 ΩR2 = 5 ΩR3 = 3 ΩR4 = 25 ΩR5 = 30 Ω
VB = V
6.Hard
R1​ = 3 ΩR3​ = 25 Ω+−V1​5 VR2​10 ΩAR4​12 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 = 5 VR1 = 3 ΩR2 = 10 ΩR3 = 25 ΩR4 = 12 Ωg = 0.1 A/V
VA = V

Answer key

  1. 1. IR1 = −0.6 A
  2. 2. IR2 = −1.398 A
  3. 3. Ix = 2.6 A
  4. 4. VA = 11.08 V
  5. 5. VB = −5.765 V
  6. 6. VA = 3.895 V

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