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​12 VR2​5 ΩAab

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

V1 = 12 VR1 = 10 ΩR2 = 5 Ω
Vth = V
2.Easy
R1​ = 12 Ω+−V1​8 VR2​3 ΩAab

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

V1 = 8 VR1 = 12 ΩR2 = 3 Ω
Rth = Ω
3.Medium
R1​ = 20 ΩR3​ = 8 Ω+−V1​30 VR2​12 ΩARL​3 ΩIL​B

A load RL = 3 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 = 12 ΩR3 = 8 ΩRL = 3 Ω
IL = A
4.Medium
R1​ = 2 ΩR3​ = 8 Ω+−V1​10 VR2​15 ΩAab

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

V1 = 10 VR1 = 2 ΩR2 = 15 ΩR3 = 8 Ω
IN = A
5.Hard
R1​ = 30 ΩR3​ = 10 Ω+−V1​5 VR2​2 ΩAIs​1 ABRL​5 ΩIL​

A load RL = 5 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 5 VIs = 1 AR1 = 30 ΩR2 = 2 ΩR3 = 10 ΩRL = 5 Ω
PL = W
6.Hard
R1​ = 6 ΩR3​ = 30 Ω+−V1​9 VR2​8 ΩAIs​0.5 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 = 9 VIs = 0.5 AR1 = 6 ΩR2 = 8 ΩR3 = 30 ΩRL = 4 Ω
PL = W

Answer key

  1. 1. Vth = 4 V
  2. 2. Rth = 2.4 Ω
  3. 3. IL = 0.6081 A
  4. 4. IN = 0.9036 A
  5. 5. PL = 2.608 W
  6. 6. PL = 1.364 W

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