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​ = 3 ΩR2​ = 6 Ω+−V1​10 VR3​4 ΩAR4​8 Ω+−VR4​BI1​I2​

Use mesh analysis to find the voltage VR4 across R4 with the polarity shown.

V1 = 10 VR1 = 3 ΩR2 = 6 ΩR3 = 4 ΩR4 = 8 Ω
VR4 = V
2.Easy
R1​ = 3 ΩR2​ = 4 ΩIR2​+−V1​20 VR3​8 ΩAR4​4 ΩBI1​I2​

Use mesh analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 20 VR1 = 3 ΩR2 = 4 ΩR3 = 8 ΩR4 = 4 Ω
IR2 = A
3.Medium
R1​ = 5 ΩR2​ = 15 Ω+−V1​12 VR3​5 ΩA+−V2​9 VI1​I2​

Use mesh analysis to find the mesh current I2 (clockwise).

V1 = 12 VV2 = 9 VR1 = 5 ΩR2 = 15 ΩR3 = 5 Ω
I2 = A
4.Medium
R1​ = 2 ΩR2​ = 15 Ω+−V1​9 VR3​6 ΩA+−V2​9 VI1​I2​

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

V1 = 9 VV2 = 9 VR1 = 2 ΩR2 = 15 ΩR3 = 6 Ω
I1 = A
5.Hard
R1​ = 20 ΩR2​ = 4 ΩR3​ = 12 Ω+−V1​5 VR4​10 ΩAR5​30 ΩIR5​B+−V2​24 VI1​I2​I3​

Use mesh analysis to find the current IR5 through R5 in the direction of the arrow.

V1 = 5 VV2 = 24 VR1 = 20 ΩR2 = 4 ΩR3 = 12 ΩR4 = 10 ΩR5 = 30 Ω
IR5 = A
6.Hard
R1​ = 12 ΩR2​ = 20 Ω+−VR2​R3​ = 4 Ω+−V1​18 VR4​15 ΩAR5​8 ΩB+−V2​12 VI1​I2​I3​

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

V1 = 18 VV2 = 12 VR1 = 12 ΩR2 = 20 ΩR3 = 4 ΩR4 = 15 ΩR5 = 8 Ω
VR2 = V

Answer key

  1. 1. VR4 = 2.909 V
  2. 2. IR2 = 1.429 A
  3. 3. I2 = −0.1714 A
  4. 4. I1 = 1.023 A
  5. 5. IR5 = 0.3416 A
  6. 6. VR2 = 1.364 V

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