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​ = 8 Ω+−V1​10 VR2​6 ΩAab

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

V1 = 10 VR1 = 8 ΩR2 = 6 Ω
Rth = Ω
2.Easy
R1​ = 8 Ω+−V1​12 VR2​8 ΩAab

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

V1 = 12 VR1 = 8 ΩR2 = 8 Ω
Vth = V
3.Medium
R1​ = 15 ΩR3​ = 4 Ω+−V1​6 VR2​3 ΩARL​6 ΩIL​B

A load RL = 6 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 6 VR1 = 15 ΩR2 = 3 ΩR3 = 4 ΩRL = 6 Ω
IL = A
4.Medium
R1​ = 10 ΩR3​ = 5 Ω+−V1​18 VR2​6 ΩARL​20 ΩIL​B

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 = 18 VR1 = 10 ΩR2 = 6 ΩR3 = 5 ΩRL = 20 Ω
IL = A
5.Hard
R1​ = 20 ΩR3​ = 12 Ω+−V1​36 VR2​15 ΩAIs​2.5 ABRL​15 ΩIL​

A load RL = 15 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 36 VIs = 2.5 AR1 = 20 ΩR2 = 15 ΩR3 = 12 ΩRL = 15 Ω
PL = W
6.Hard
R1​ = 4 ΩR3​ = 3 Ω+−V1​18 VR2​2 ΩAIs​2.5 ABab

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

V1 = 18 VIs = 2.5 AR1 = 4 ΩR2 = 2 ΩR3 = 3 Ω
IN = A

Answer key

  1. 1. Rth = 3.429 Ω
  2. 2. Vth = 6 V
  3. 3. IL = 0.08 A
  4. 4. IL = 0.2348 A
  5. 5. PL = 52.99 W
  6. 6. IN = 3.885 A

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