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​12 VR2​2 ΩAab

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

V1 = 12 VR1 = 12 ΩR2 = 2 Ω
Vth = V
2.Easy
R1​ = 10 Ω+−V1​8 VR2​3 ΩAab

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

V1 = 8 VR1 = 10 ΩR2 = 3 Ω
IN = A
3.Medium
R1​ = 10 ΩR3​ = 2 Ω+−V1​18 VR2​10 ΩARL​2 ΩIL​B

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 = 18 VR1 = 10 ΩR2 = 10 ΩR3 = 2 ΩRL = 2 Ω
IL = A
4.Medium
R1​ = 10 ΩR3​ = 6 Ω+−V1​24 VR2​3 ΩAab

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

V1 = 24 VR1 = 10 ΩR2 = 3 ΩR3 = 6 Ω
Rth = Ω
5.Hard
R1​ = 10 ΩR3​ = 10 Ω+−V1​5 VR2​12 ΩAIs​0.5 ABRL​15 ΩIL​

A load RL = 15 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 5 VIs = 0.5 AR1 = 10 ΩR2 = 12 ΩR3 = 10 ΩRL = 15 Ω
PL = W
6.Hard
R1​ = 12 ΩR3​ = 6 Ω+−V1​36 VR2​5 ΩAIs​1.5 ABRL​2 ΩIL​

A load RL = 2 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 36 VIs = 1.5 AR1 = 12 ΩR2 = 5 ΩR3 = 6 ΩRL = 2 Ω
PL = W

Answer key

  1. 1. Vth = 1.714 V
  2. 2. IN = 0.8 A
  3. 3. IL = 1 A
  4. 4. Rth = 8.308 Ω
  5. 5. PL = 0.4043 W
  6. 6. PL = 9.315 W

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