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​10 VR2​10 ΩAab

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

V1 = 10 VR1 = 6 ΩR2 = 10 Ω
Vth = V
2.Easy
R1​ = 5 Ω+−V1​20 VR2​8 ΩAab

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

V1 = 20 VR1 = 5 ΩR2 = 8 Ω
IN = A
3.Medium
R1​ = 6 ΩR3​ = 5 Ω+−V1​15 VR2​12 ΩAab

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

V1 = 15 VR1 = 6 ΩR2 = 12 ΩR3 = 5 Ω
Rth = Ω
4.Medium
R1​ = 15 ΩR3​ = 10 Ω+−V1​10 VR2​2 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 = 10 VR1 = 15 ΩR2 = 2 ΩR3 = 10 ΩRL = 20 Ω
IL = A
5.Hard
R1​ = 3 ΩR3​ = 30 Ω+−V1​18 VR2​30 ΩAIs​0.5 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 = 18 VIs = 0.5 AR1 = 3 ΩR2 = 30 ΩR3 = 30 ΩRL = 10 Ω
IL = A
6.Hard
R1​ = 8 ΩR3​ = 30 Ω+−V1​5 VR2​2 ΩAIs​4 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 = 5 VIs = 4 AR1 = 8 ΩR2 = 2 ΩR3 = 30 ΩRL = 8 Ω
PL = W

Answer key

  1. 1. Vth = 6.25 V
  2. 2. IN = 4 A
  3. 3. Rth = 9 Ω
  4. 4. IL = 0.03704 A
  5. 5. IL = 0.766 A
  6. 6. PL = 80.22 W

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