Mesh analysis worksheet with answers

Free printable Mesh analysis 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 ΩR2​ = 4 Ω+−V1​15 VR3​6 ΩAR4​12 ΩBI1​I2​

Use mesh analysis to find the mesh current I1 (clockwise).

V1 = 15 VR1 = 8 ΩR2 = 4 ΩR3 = 6 ΩR4 = 12 Ω
I1 = A
2.Easy
R1​ = 4 ΩR2​ = 5 Ω+−V1​15 VR3​2 ΩIR3​AR4​8 ΩBI1​I2​

Use mesh analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 15 VR1 = 4 ΩR2 = 5 ΩR3 = 2 ΩR4 = 8 Ω
IR3 = A
3.Medium
R1​ = 3 ΩIR1​R2​ = 4 Ω+−V1​24 VR3​15 ΩA+−V2​9 VI1​I2​

Use mesh analysis to find the current IR1 through R1 in the direction of the arrow.

V1 = 24 VV2 = 9 VR1 = 3 ΩR2 = 4 ΩR3 = 15 Ω
IR1 = A
4.Medium
R1​ = 12 ΩR2​ = 8 Ω+−VR2​+−V1​15 VR3​12 ΩA+−V2​30 VI1​I2​

Use mesh analysis to find the voltage VR2 across R2 with the polarity shown.

V1 = 15 VV2 = 30 VR1 = 12 ΩR2 = 8 ΩR3 = 12 Ω
VR2 = V
5.Hard
R1​ = 4 ΩR2​ = 5 ΩR3​ = 3 Ω+−V1​10 VR4​5 ΩAR5​3 ΩB+−V2​15 VI1​I2​I3​

Use mesh analysis to find the mesh current I3 (clockwise).

V1 = 10 VV2 = 15 VR1 = 4 ΩR2 = 5 ΩR3 = 3 ΩR4 = 5 ΩR5 = 3 Ω
I3 = A
6.Hard
R1​ = 2 ΩR2​ = 5 ΩR3​ = 3 Ω+−V1​36 VR4​4 ΩAR5​6 Ω+−VR5​B+−V2​10 VI1​I2​I3​

Use mesh analysis to find the voltage VR5 across R5 with the polarity shown.

V1 = 36 VV2 = 10 VR1 = 2 ΩR2 = 5 ΩR3 = 3 ΩR4 = 4 ΩR5 = 6 Ω
VR5 = V

Answer key

  1. 1. I1 = 1.213 A
  2. 2. IR3 = 2.267 A
  3. 3. IR1 = 2.744 A
  4. 4. VR2 = −12.86 V
  5. 5. I3 = −2.611 A
  6. 6. VR5 = 10.83 V

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