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​ = 12 ΩR2​ = 8 Ω+−V1​12 VR3​8 ΩAR4​4 ΩBI1​I2​

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

V1 = 12 VR1 = 12 ΩR2 = 8 ΩR3 = 8 ΩR4 = 4 Ω
I2 = A
2.Easy
R1​ = 6 ΩR2​ = 4 Ω+−V1​20 VR3​6 ΩAR4​10 ΩBI1​I2​

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

V1 = 20 VR1 = 6 ΩR2 = 4 ΩR3 = 6 ΩR4 = 10 Ω
I1 = A
3.Medium
R1​ = 4 ΩR2​ = 10 ΩIR2​+−V1​6 VR3​4 ΩA+−V2​9 VI1​I2​

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

V1 = 6 VV2 = 9 VR1 = 4 ΩR2 = 10 ΩR3 = 4 Ω
IR2 = A
4.Medium
R1​ = 20 ΩR2​ = 5 Ω+−V1​30 VR3​2 Ω+−VR3​A+−V2​18 VI1​I2​

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

V1 = 30 VV2 = 18 VR1 = 20 ΩR2 = 5 ΩR3 = 2 Ω
VR3 = V
5.Hard
R1​ = 10 ΩR2​ = 10 ΩR3​ = 4 ΩIR3​+−V1​15 VR4​5 ΩAR5​6 ΩB+−V2​10 VI1​I2​I3​

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

V1 = 15 VV2 = 10 VR1 = 10 ΩR2 = 10 ΩR3 = 4 ΩR4 = 5 ΩR5 = 6 Ω
IR3 = A
6.Hard
R1​ = 20 ΩR2​ = 2 ΩR3​ = 3 Ω+−V1​6 VR4​12 ΩAR5​5 ΩB+−V2​6 VI1​I2​I3​

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

V1 = 6 VV2 = 6 VR1 = 20 ΩR2 = 2 ΩR3 = 3 ΩR4 = 12 ΩR5 = 5 Ω
I3 = A

Answer key

  1. 1. I2 = 0.2857 A
  2. 2. I1 = 1.961 A
  3. 3. IR2 = −0.5 A
  4. 4. VR3 = 6.8 V
  5. 5. IR3 = −1.038 A
  6. 6. I3 = −0.8324 A

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