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​ = 6 Ω+−VR1​R2​ = 12 Ω+−V1​10 VR3​10 ΩAR4​5 ΩBI1​I2​

Use mesh analysis to find the voltage VR1 across R1 with the polarity shown.

V1 = 10 VR1 = 6 ΩR2 = 12 ΩR3 = 10 ΩR4 = 5 Ω
VR1 = V
2.Easy
R1​ = 4 ΩIR1​R2​ = 2 Ω+−V1​6 VR3​5 ΩAR4​4 ΩBI1​I2​

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

V1 = 6 VR1 = 4 ΩR2 = 2 ΩR3 = 5 ΩR4 = 4 Ω
IR1 = A
3.Medium
R1​ = 15 ΩR2​ = 8 Ω+−V1​30 VR3​6 ΩA+−V2​9 VI1​I2​

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

V1 = 30 VV2 = 9 VR1 = 15 ΩR2 = 8 ΩR3 = 6 Ω
I1 = A
4.Medium
R1​ = 3 ΩR2​ = 3 Ω+−V1​24 VR3​8 ΩA+−V2​30 VI1​I2​

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

V1 = 24 VV2 = 30 VR1 = 3 ΩR2 = 3 ΩR3 = 8 Ω
I2 = A
5.Hard
R1​ = 8 ΩR2​ = 30 Ω+−VR2​R3​ = 2 Ω+−V1​12 VR4​10 ΩAR5​8 ΩB+−V2​12 VI1​I2​I3​

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

V1 = 12 VV2 = 12 VR1 = 8 ΩR2 = 30 ΩR3 = 2 ΩR4 = 10 ΩR5 = 8 Ω
VR2 = V
6.Hard
R1​ = 4 ΩR2​ = 15 ΩIR2​R3​ = 10 Ω+−V1​30 VR4​8 ΩAR5​2 ΩB+−V2​15 VI1​I2​I3​

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

V1 = 30 VV2 = 15 VR1 = 4 ΩR2 = 15 ΩR3 = 10 ΩR4 = 8 ΩR5 = 2 Ω
IR2 = A

Answer key

  1. 1. VR1 = 4.88 V
  2. 2. IR1 = 0.8919 A
  3. 3. I1 = 1.419 A
  4. 4. I2 = −2.421 A
  5. 5. VR2 = −2.441 V
  6. 6. IR2 = 0.9052 A

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