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​ = 10 Ω+−V1​18 VR2​12 ΩAab

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

V1 = 18 VR1 = 10 ΩR2 = 12 Ω
IN = A
2.Easy
R1​ = 10 Ω+−V1​20 VR2​4 ΩAab

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

V1 = 20 VR1 = 10 ΩR2 = 4 Ω
Rth = Ω
3.Medium
R1​ = 15 ΩR3​ = 5 Ω+−V1​9 VR2​20 ΩAab

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

V1 = 9 VR1 = 15 ΩR2 = 20 ΩR3 = 5 Ω
Vth = V
4.Medium
R1​ = 4 ΩR3​ = 6 Ω+−V1​15 VR2​10 ΩARL​15 ΩIL​B

A load RL = 15 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 = 4 ΩR2 = 10 ΩR3 = 6 ΩRL = 15 Ω
IL = A
5.Hard
R1​ = 5 ΩR3​ = 15 Ω+−V1​10 VR2​5 ΩAIs​5 ABRL​6 ΩIL​

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 = 10 VIs = 5 AR1 = 5 ΩR2 = 5 ΩR3 = 15 ΩRL = 6 Ω
IL = A
6.Hard
R1​ = 25 ΩR3​ = 6 Ω+−V1​18 VR2​15 ΩAIs​1 ABRL​30 ΩIL​

A load RL = 30 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 18 VIs = 1 AR1 = 25 ΩR2 = 15 ΩR3 = 6 ΩRL = 30 Ω
PL = W

Answer key

  1. 1. IN = 1.8 A
  2. 2. Rth = 2.857 Ω
  3. 3. Vth = 5.143 V
  4. 4. IL = 0.4491 A
  5. 5. IL = 3.936 A
  6. 6. PL = 7.133 W

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