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​ = 6 Ω+−V1​18 VR2​10 ΩAab

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

V1 = 18 VR1 = 6 ΩR2 = 10 Ω
Rth = Ω
2.Easy
R1​ = 2 Ω+−V1​12 VR2​4 ΩAab

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

V1 = 12 VR1 = 2 ΩR2 = 4 Ω
Vth = V
3.Medium
R1​ = 20 ΩR3​ = 5 Ω+−V1​24 VR2​8 ΩAab

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

V1 = 24 VR1 = 20 ΩR2 = 8 ΩR3 = 5 Ω
IN = A
4.Medium
R1​ = 6 ΩR3​ = 2 Ω+−V1​30 VR2​2 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 = 30 VR1 = 6 ΩR2 = 2 ΩR3 = 2 ΩRL = 2 Ω
IL = A
5.Hard
R1​ = 20 ΩR3​ = 3 Ω+−V1​9 VR2​12 ΩAIs​1.5 ABRL​30 ΩIL​

A load RL = 30 Ω is connected across a–b. Replace the rest of the circuit with its Thévenin equivalent and find the load current IL.

V1 = 9 VIs = 1.5 AR1 = 20 ΩR2 = 12 ΩR3 = 3 ΩRL = 30 Ω
IL = A
6.Hard
R1​ = 30 ΩR3​ = 25 Ω+−V1​12 VR2​25 ΩAIs​1 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 = 12 VIs = 1 AR1 = 30 ΩR2 = 25 ΩR3 = 25 ΩRL = 30 Ω
PL = W

Answer key

  1. 1. Rth = 3.75 Ω
  2. 2. Vth = 8 V
  3. 3. IN = 0.64 A
  4. 4. IL = 1.364 A
  5. 5. IL = −0.3056 A
  6. 6. PL = 12.38 W

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