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​ = 4 Ω+−V1​10 VR2​12 ΩAab

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

V1 = 10 VR1 = 4 ΩR2 = 12 Ω
Vth = V
2.Easy
R1​ = 5 Ω+−V1​12 VR2​2 ΩAab

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

V1 = 12 VR1 = 5 ΩR2 = 2 Ω
IN = A
3.Medium
R1​ = 8 ΩR3​ = 12 Ω+−V1​30 VR2​2 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 = 30 VR1 = 8 ΩR2 = 2 ΩR3 = 12 ΩRL = 15 Ω
IL = A
4.Medium
R1​ = 15 ΩR3​ = 6 Ω+−V1​30 VR2​4 ΩAab

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

V1 = 30 VR1 = 15 ΩR2 = 4 ΩR3 = 6 Ω
Rth = Ω
5.Hard
R1​ = 3 ΩR3​ = 5 Ω+−V1​6 VR2​5 ΩAIs​2.5 ABRL​10 ΩIL​

A load RL = 10 Ω is connected across a–b. Use a Thévenin equivalent to find the power PL delivered to the load.

V1 = 6 VIs = 2.5 AR1 = 3 ΩR2 = 5 ΩR3 = 5 ΩRL = 10 Ω
PL = W
6.Hard
R1​ = 20 ΩR3​ = 5 Ω+−V1​15 VR2​10 ΩAIs​3 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 = 15 VIs = 3 AR1 = 20 ΩR2 = 10 ΩR3 = 5 ΩRL = 30 Ω
PL = W

Answer key

  1. 1. Vth = 7.5 V
  2. 2. IN = 2.4 A
  3. 3. IL = 0.2098 A
  4. 4. Rth = 9.158 Ω
  5. 5. PL = 15.39 W
  6. 6. PL = 27.65 W

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