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​ = 4 Ω+−VR1​R2​ = 3 Ω+−V1​10 VR3​2 ΩAR4​12 ΩBI1​I2​

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

V1 = 10 VR1 = 4 ΩR2 = 3 ΩR3 = 2 ΩR4 = 12 Ω
VR1 = V
2.Easy
R1​ = 10 ΩR2​ = 6 Ω+−V1​8 VR3​4 ΩAR4​8 Ω+−VR4​BI1​I2​

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

V1 = 8 VR1 = 10 ΩR2 = 6 ΩR3 = 4 ΩR4 = 8 Ω
VR4 = V
3.Medium
R1​ = 20 ΩIR1​R2​ = 6 Ω+−V1​10 VR3​12 ΩA+−V2​6 VI1​I2​

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

V1 = 10 VV2 = 6 VR1 = 20 ΩR2 = 6 ΩR3 = 12 Ω
IR1 = A
4.Medium
R1​ = 2 ΩR2​ = 6 Ω+−VR2​+−V1​15 VR3​15 ΩA+−V2​18 VI1​I2​

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

V1 = 15 VV2 = 18 VR1 = 2 ΩR2 = 6 ΩR3 = 15 Ω
VR2 = V
5.Hard
R1​ = 8 ΩR2​ = 5 ΩR3​ = 3 Ω+−V1​18 VR4​12 ΩAR5​4 ΩB+−V2​5 VI1​I2​I3​

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

V1 = 18 VV2 = 5 VR1 = 8 ΩR2 = 5 ΩR3 = 3 ΩR4 = 12 ΩR5 = 4 Ω
I3 = A
6.Hard
R1​ = 30 ΩR2​ = 20 ΩR3​ = 15 Ω+−V1​5 VR4​3 ΩAR5​6 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 = 30 ΩR2 = 20 ΩR3 = 15 ΩR4 = 3 ΩR5 = 6 Ω
IR5 = A

Answer key

  1. 1. VR1 = 6.939 V
  2. 2. VR4 = 1.085 V
  3. 3. IR1 = 0.25 A
  4. 4. VR2 = −3.682 V
  5. 5. I3 = −0.3201 A
  6. 6. IR5 = 0.9736 A

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