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​ = 5 Ω+−VR1​R2​ = 3 Ω+−V1​18 VR3​8 ΩAR4​8 ΩBI1​I2​

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

V1 = 18 VR1 = 5 ΩR2 = 3 ΩR3 = 8 ΩR4 = 8 Ω
VR1 = V
2.Easy
R1​ = 4 ΩR2​ = 4 Ω+−V1​15 VR3​8 ΩAR4​8 ΩIR4​BI1​I2​

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

V1 = 15 VR1 = 4 ΩR2 = 4 ΩR3 = 8 ΩR4 = 8 Ω
IR4 = A
3.Medium
R1​ = 20 ΩR2​ = 5 Ω+−V1​9 VR3​12 ΩA+−V2​9 VI1​I2​

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

V1 = 9 VV2 = 9 VR1 = 20 ΩR2 = 5 ΩR3 = 12 Ω
I2 = A
4.Medium
R1​ = 8 ΩR2​ = 3 Ω+−V1​15 VR3​8 ΩIR3​A+−V2​6 VI1​I2​

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

V1 = 15 VV2 = 6 VR1 = 8 ΩR2 = 3 ΩR3 = 8 Ω
IR3 = A
5.Hard
R1​ = 8 ΩR2​ = 4 ΩR3​ = 10 Ω+−VR3​+−V1​36 VR4​20 ΩAR5​12 ΩB+−V2​30 VI1​I2​I3​

Use mesh analysis to find the voltage VR3 across R3 with the polarity shown.

V1 = 36 VV2 = 30 VR1 = 8 ΩR2 = 4 ΩR3 = 10 ΩR4 = 20 ΩR5 = 12 Ω
VR3 = V
6.Hard
R1​ = 8 ΩR2​ = 12 ΩR3​ = 15 Ω+−V1​18 VR4​5 ΩAR5​8 ΩB+−V2​9 VI1​I2​I3​

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

V1 = 18 VV2 = 9 VR1 = 8 ΩR2 = 12 ΩR3 = 15 ΩR4 = 5 ΩR5 = 8 Ω
I3 = A

Answer key

  1. 1. VR1 = 9.344 V
  2. 2. IR4 = 0.6818 A
  3. 3. I2 = −0.45 A
  4. 4. IR3 = 0.8304 A
  5. 5. VR3 = −10.27 V
  6. 6. I3 = −0.3263 A

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