Thévenin & Norton worksheet with answers

Free printable Thévenin & Norton 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​15 VR2​12 ΩAab

Find the Thévenin voltage Vth seen from terminals a–b.

V1 = 15 VR1 = 3 ΩR2 = 12 Ω
Vth = V
2.Easy
R1​ = 10 Ω+−V1​18 VR2​5 ΩAab

Find the Norton current IN: the current that flows from a to b if the terminals are shorted.

V1 = 18 VR1 = 10 ΩR2 = 5 Ω
IN = A
3.Medium
R1​ = 10 ΩR3​ = 4 Ω+−V1​9 VR2​4 ΩAab

Find the Thévenin resistance Rth seen from terminals a–b.

V1 = 9 VR1 = 10 ΩR2 = 4 ΩR3 = 4 Ω
Rth = Ω
4.Medium
R1​ = 5 ΩR3​ = 8 Ω+−V1​24 VR2​5 ΩARL​3 ΩIL​B

A load RL = 3 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 24 VR1 = 5 ΩR2 = 5 ΩR3 = 8 ΩRL = 3 Ω
IL = A
5.Hard
R1​ = 10 ΩR3​ = 10 Ω+−V1​30 VR2​20 ΩAIs​6 ABRL​4 ΩIL​

A load RL = 4 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 30 VIs = 6 AR1 = 10 ΩR2 = 20 ΩR3 = 10 ΩRL = 4 Ω
IL = A
6.Hard
R1​ = 10 ΩR3​ = 25 Ω+−V1​36 VR2​15 ΩAIs​2 ABRL​20 ΩIL​

A load RL = 20 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 36 VIs = 2 AR1 = 10 ΩR2 = 15 ΩR3 = 25 ΩRL = 20 Ω
IL = A

Answer key

  1. 1. Vth = 12 V
  2. 2. IN = 1.8 A
  3. 3. Rth = 6.857 Ω
  4. 4. IL = 0.8889 A
  5. 5. IL = −3.871 A
  6. 6. IL = −0.7922 A

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