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​ = 8 Ω+−V1​18 VR2​10 ΩAab

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

V1 = 18 VR1 = 8 ΩR2 = 10 Ω
Rth = Ω
2.Easy
R1​ = 2 Ω+−V1​24 VR2​6 ΩAab

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

V1 = 24 VR1 = 2 ΩR2 = 6 Ω
IN = A
3.Medium
R1​ = 20 ΩR3​ = 8 Ω+−V1​15 VR2​3 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 = 20 ΩR2 = 3 ΩR3 = 8 ΩRL = 15 Ω
IL = A
4.Medium
R1​ = 20 ΩR3​ = 8 Ω+−V1​30 VR2​8 ΩAab

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

V1 = 30 VR1 = 20 ΩR2 = 8 ΩR3 = 8 Ω
Vth = V
5.Hard
R1​ = 4 ΩR3​ = 3 Ω+−V1​18 VR2​8 ΩAIs​1 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 = 18 VIs = 1 AR1 = 4 ΩR2 = 8 ΩR3 = 3 ΩRL = 4 Ω
PL = W
6.Hard
R1​ = 20 ΩR3​ = 10 Ω+−V1​30 VR2​15 ΩAIs​0.5 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 = 30 VIs = 0.5 AR1 = 20 ΩR2 = 15 ΩR3 = 10 ΩRL = 30 Ω
PL = W

Answer key

  1. 1. Rth = 4.444 Ω
  2. 2. IN = 12 A
  3. 3. IL = 0.0764 A
  4. 4. Vth = 8.571 V
  5. 5. PL = 1.717 W
  6. 6. PL = 6.235 W

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