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​20 VR2​3 ΩAab

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

V1 = 20 VR1 = 12 ΩR2 = 3 Ω
Vth = V
2.Easy
R1​ = 5 Ω+−V1​20 VR2​5 ΩAab

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

V1 = 20 VR1 = 5 ΩR2 = 5 Ω
IN = A
3.Medium
R1​ = 2 ΩR3​ = 15 Ω+−V1​9 VR2​15 ΩARL​8 ΩIL​B

A load RL = 8 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 9 VR1 = 2 ΩR2 = 15 ΩR3 = 15 ΩRL = 8 Ω
IL = A
4.Medium
R1​ = 20 ΩR3​ = 8 Ω+−V1​10 VR2​12 ΩAab

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

V1 = 10 VR1 = 20 ΩR2 = 12 ΩR3 = 8 Ω
Rth = Ω
5.Hard
R1​ = 2 ΩR3​ = 2 Ω+−V1​9 VR2​20 ΩAIs​2 ABRL​10 ΩIL​

A load RL = 10 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 9 VIs = 2 AR1 = 2 ΩR2 = 20 ΩR3 = 2 ΩRL = 10 Ω
PL = W
6.Hard
R1​ = 30 ΩR3​ = 6 Ω+−V1​9 VR2​3 ΩAIs​2 ABRL​10 ΩIL​

A load RL = 10 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 9 VIs = 2 AR1 = 30 ΩR2 = 3 ΩR3 = 6 ΩRL = 10 Ω
IL = A

Answer key

  1. 1. Vth = 4 V
  2. 2. IN = 4 A
  3. 3. IL = 0.3207 A
  4. 4. Rth = 15.5 Ω
  5. 5. PL = 13.1 W
  6. 6. IL = 0.9757 A

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