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​ = 3 Ω+−V1​8 VR3​12 ΩAR4​10 ΩBI1​I2​

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

V1 = 8 VR1 = 6 ΩR2 = 3 ΩR3 = 12 ΩR4 = 10 Ω
VR1 = V
2.Easy
R1​ = 2 ΩR2​ = 12 Ω+−V1​12 VR3​12 ΩAR4​5 ΩIR4​BI1​I2​

Use mesh analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 12 VR1 = 2 ΩR2 = 12 ΩR3 = 12 ΩR4 = 5 Ω
IR4 = A
3.Medium
R1​ = 10 ΩR2​ = 6 Ω+−V1​6 VR3​15 ΩA+−V2​24 VI1​I2​

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

V1 = 6 VV2 = 24 VR1 = 10 ΩR2 = 6 ΩR3 = 15 Ω
I2 = A
4.Medium
R1​ = 20 ΩR2​ = 4 Ω+−V1​6 VR3​3 ΩIR3​A+−V2​12 VI1​I2​

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

V1 = 6 VV2 = 12 VR1 = 20 ΩR2 = 4 ΩR3 = 3 Ω
IR3 = A
5.Hard
R1​ = 4 ΩR2​ = 6 ΩR3​ = 20 Ω+−V1​9 VR4​20 Ω+−VR4​AR5​4 ΩB+−V2​10 VI1​I2​I3​

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

V1 = 9 VV2 = 10 VR1 = 4 ΩR2 = 6 ΩR3 = 20 ΩR4 = 20 ΩR5 = 4 Ω
VR4 = V
6.Hard
R1​ = 5 ΩIR1​R2​ = 20 ΩR3​ = 15 Ω+−V1​36 VR4​8 ΩAR5​2 ΩB+−V2​24 VI1​I2​I3​

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

V1 = 36 VV2 = 24 VR1 = 5 ΩR2 = 20 ΩR3 = 15 ΩR4 = 8 ΩR5 = 2 Ω
IR1 = A

Answer key

  1. 1. VR1 = 3.922 V
  2. 2. IR4 = 0.5496 A
  3. 3. I2 = −1.7 A
  4. 4. IR3 = 1.737 A
  5. 5. VR4 = 5.965 V
  6. 6. IR1 = 3.248 A

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