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​6 VR2​5 ΩAab

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

V1 = 6 VR1 = 2 ΩR2 = 5 Ω
Vth = V
2.Easy
R1​ = 6 Ω+−V1​15 VR2​4 ΩAab

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

V1 = 15 VR1 = 6 ΩR2 = 4 Ω
Rth = Ω
3.Medium
R1​ = 4 ΩR3​ = 2 Ω+−V1​15 VR2​8 ΩARL​6 ΩIL​B

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 = 15 VR1 = 4 ΩR2 = 8 ΩR3 = 2 ΩRL = 6 Ω
IL = A
4.Medium
R1​ = 10 ΩR3​ = 5 Ω+−V1​9 VR2​15 ΩAab

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

V1 = 9 VR1 = 10 ΩR2 = 15 ΩR3 = 5 Ω
IN = A
5.Hard
R1​ = 2 ΩR3​ = 15 Ω+−V1​24 VR2​4 ΩAIs​1 ABRL​20 ΩIL​

A load RL = 20 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 24 VIs = 1 AR1 = 2 ΩR2 = 4 ΩR3 = 15 ΩRL = 20 Ω
PL = W
6.Hard
R1​ = 3 ΩR3​ = 5 Ω+−V1​18 VR2​12 ΩAIs​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 = 18 VIs = 5 AR1 = 3 ΩR2 = 12 ΩR3 = 5 ΩRL = 2 Ω
PL = W

Answer key

  1. 1. Vth = 4.286 V
  2. 2. Rth = 2.4 Ω
  3. 3. IL = 0.9375 A
  4. 4. IN = 0.4909 A
  5. 5. PL = 15.84 W
  6. 6. PL = 59.8 W

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