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​ = 3 Ω+−VR1​R2​ = 10 Ω+−V1​10 VR3​8 ΩAR4​6 ΩBI1​I2​

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

V1 = 10 VR1 = 3 ΩR2 = 10 ΩR3 = 8 ΩR4 = 6 Ω
VR1 = V
2.Easy
R1​ = 5 ΩR2​ = 4 Ω+−V1​24 VR3​3 ΩAR4​8 ΩBI1​I2​

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

V1 = 24 VR1 = 5 ΩR2 = 4 ΩR3 = 3 ΩR4 = 8 Ω
I1 = A
3.Medium
R1​ = 15 ΩIR1​R2​ = 6 Ω+−V1​10 VR3​2 ΩA+−V2​9 VI1​I2​

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

V1 = 10 VV2 = 9 VR1 = 15 ΩR2 = 6 ΩR3 = 2 Ω
IR1 = A
4.Medium
R1​ = 3 ΩR2​ = 3 Ω+−V1​12 VR3​3 ΩA+−V2​30 VI1​I2​

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

V1 = 12 VV2 = 30 VR1 = 3 ΩR2 = 3 ΩR3 = 3 Ω
I2 = A
5.Hard
R1​ = 12 ΩR2​ = 15 ΩR3​ = 2 Ω+−V1​10 VR4​15 ΩAR5​12 ΩIR5​B+−V2​5 VI1​I2​I3​

Use mesh analysis to find the current IR5 through R5 in the direction of the arrow.

V1 = 10 VV2 = 5 VR1 = 12 ΩR2 = 15 ΩR3 = 2 ΩR4 = 15 ΩR5 = 12 Ω
IR5 = A
6.Hard
R1​ = 10 ΩR2​ = 2 Ω+−VR2​R3​ = 12 Ω+−V1​36 VR4​10 ΩAR5​30 ΩB+−V2​36 VI1​I2​I3​

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

V1 = 36 VV2 = 36 VR1 = 10 ΩR2 = 2 ΩR3 = 12 ΩR4 = 10 ΩR5 = 30 Ω
VR2 = V

Answer key

  1. 1. VR1 = 3.6 V
  2. 2. I1 = 3.243 A
  3. 3. IR1 = 0.4697 A
  4. 4. I2 = −5.333 A
  5. 5. IR5 = 0.3649 A
  6. 6. VR2 = −0.9908 V

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