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​3 Ω+−V1​20 VR2​10 Ω+−V2​12 VR3​8 Ω+−V3​12 VA

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

V1 = 20 VR1 = 3 ΩV2 = 12 VR2 = 10 ΩV3 = 12 VR3 = 8 Ω
VA = V
2.Easy
R1​ = 6 Ω+−V1​6 VR2​?AIs​1 A

The node voltage at A is measured as VA = 2 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 1 AR1 = 6 ΩVA = 2 V
R2 = Ω
3.Medium
R1​12 Ω+−V1​18 VR2​10 Ω+−V2​30 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 = 18 VR1 = 12 ΩV2 = 30 VR2 = 10 ΩV3 = 15 VR3 = 20 Ω
I3 = A
4.Medium
R1​ = 15 ΩR3​ = 3 ΩIR3​+−V1​12 VR2​5 ΩAR4​8 ΩBIs​2.5 A

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

V1 = 12 VIs = 2.5 AR1 = 15 ΩR2 = 5 ΩR3 = 3 ΩR4 = 8 Ω
IR3 = A
5.Hard
R1​ = 5 ΩR3​ = 10 Ω+−V1​30 VR2​6 ΩAR4​5 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 = 30 VR1 = 5 ΩR2 = 6 ΩR3 = 10 ΩR4 = 5 Ωg = 0.1 A/V
VA = V
6.Hard
R1​ = 6 ΩR3​ = 10 Ω+−V1​10 VR2​6 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 = 10 VR1 = 6 ΩR2 = 6 ΩR3 = 10 ΩR4 = 20 Ωg = 0.2 A/V
IR4 = A

Answer key

  1. 1. VA = 16.78 V
  2. 2. R2 = 1.2 Ω
  3. 3. I3 = −0.375 A
  4. 4. IR3 = 1.559 A
  5. 5. VA = 15 V
  6. 6. IR4 = 0.7143 A

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