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​ = 12 Ω+−V1​8 VR2​10 ΩAab

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

V1 = 8 VR1 = 12 ΩR2 = 10 Ω
Vth = V
2.Easy
R1​ = 3 Ω+−V1​15 VR2​2 ΩAab

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

V1 = 15 VR1 = 3 ΩR2 = 2 Ω
Rth = Ω
3.Medium
R1​ = 5 ΩR3​ = 10 Ω+−V1​15 VR2​20 ΩARL​12 ΩIL​B

A load RL = 12 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 15 VR1 = 5 ΩR2 = 20 ΩR3 = 10 ΩRL = 12 Ω
IL = A
4.Medium
R1​ = 5 ΩR3​ = 20 Ω+−V1​15 VR2​2 ΩAab

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

V1 = 15 VR1 = 5 ΩR2 = 2 ΩR3 = 20 Ω
IN = A
5.Hard
R1​ = 6 ΩR3​ = 3 Ω+−V1​36 VR2​15 ΩAIs​1 ABRL​20 ΩIL​

A load RL = 20 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 36 VIs = 1 AR1 = 6 ΩR2 = 15 ΩR3 = 3 ΩRL = 20 Ω
PL = W
6.Hard
R1​ = 12 ΩR3​ = 4 Ω+−V1​5 VR2​12 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 = 5 VIs = 2 AR1 = 12 ΩR2 = 12 ΩR3 = 4 ΩRL = 20 Ω
IL = A

Answer key

  1. 1. Vth = 3.636 V
  2. 2. Rth = 1.2 Ω
  3. 3. IL = 0.4615 A
  4. 4. IN = 0.2 A
  5. 5. PL = 29.25 W
  6. 6. IL = 0.75 A

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