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​ = 2 Ω+−V1​8 VR2​8 ΩAab

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

V1 = 8 VR1 = 2 ΩR2 = 8 Ω
IN = A
2.Easy
R1​ = 5 Ω+−V1​24 VR2​4 ΩAab

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

V1 = 24 VR1 = 5 ΩR2 = 4 Ω
Rth = Ω
3.Medium
R1​ = 20 ΩR3​ = 12 Ω+−V1​30 VR2​2 ΩARL​5 ΩIL​B

A load RL = 5 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 30 VR1 = 20 ΩR2 = 2 ΩR3 = 12 ΩRL = 5 Ω
IL = A
4.Medium
R1​ = 6 ΩR3​ = 8 Ω+−V1​9 VR2​4 ΩAab

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

V1 = 9 VR1 = 6 ΩR2 = 4 ΩR3 = 8 Ω
Vth = V
5.Hard
R1​ = 3 ΩR3​ = 5 Ω+−V1​5 VR2​15 ΩAIs​5 ABRL​12 ΩIL​

A load RL = 12 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 5 VIs = 5 AR1 = 3 ΩR2 = 15 ΩR3 = 5 ΩRL = 12 Ω
PL = W
6.Hard
R1​ = 12 ΩR3​ = 15 Ω+−V1​30 VR2​20 ΩAIs​1.5 ABRL​4 ΩIL​

A load RL = 4 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 30 VIs = 1.5 AR1 = 12 ΩR2 = 20 ΩR3 = 15 ΩRL = 4 Ω
PL = W

Answer key

  1. 1. IN = 4 A
  2. 2. Rth = 2.222 Ω
  3. 3. IL = 0.1449 A
  4. 4. Vth = 3.6 V
  5. 5. PL = 54.79 W
  6. 6. PL = 15.7 W

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