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​ = 6 Ω+−V1​6 VR2​2 ΩAab

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

V1 = 6 VR1 = 6 ΩR2 = 2 Ω
Rth = Ω
2.Easy
R1​ = 6 Ω+−V1​18 VR2​2 ΩAab

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

V1 = 18 VR1 = 6 ΩR2 = 2 Ω
IN = A
3.Medium
R1​ = 6 ΩR3​ = 5 Ω+−V1​12 VR2​15 ΩARL​4 ΩIL​B

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 = 12 VR1 = 6 ΩR2 = 15 ΩR3 = 5 ΩRL = 4 Ω
IL = A
4.Medium
R1​ = 15 ΩR3​ = 10 Ω+−V1​18 VR2​2 ΩAab

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

V1 = 18 VR1 = 15 ΩR2 = 2 ΩR3 = 10 Ω
Vth = V
5.Hard
R1​ = 3 ΩR3​ = 5 Ω+−V1​30 VR2​25 ΩAIs​5 ABRL​2 ΩIL​

A load RL = 2 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 = 5 AR1 = 3 ΩR2 = 25 ΩR3 = 5 ΩRL = 2 Ω
IL = A
6.Hard
R1​ = 5 ΩR3​ = 12 Ω+−V1​9 VR2​4 ΩAIs​6 ABRL​8 ΩIL​

A load RL = 8 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 9 VIs = 6 AR1 = 5 ΩR2 = 4 ΩR3 = 12 ΩRL = 8 Ω
PL = W

Answer key

  1. 1. Rth = 1.5 Ω
  2. 2. IN = 3 A
  3. 3. IL = 0.6452 A
  4. 4. Vth = 2.118 V
  5. 5. IL = 6.734 A
  6. 6. PL = 129.3 W

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