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​ = 8 Ω+−V1​24 VR3​4 ΩAR4​6 ΩBI1​I2​

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

V1 = 24 VR1 = 5 ΩR2 = 8 ΩR3 = 4 ΩR4 = 6 Ω
VR1 = V
2.Easy
R1​ = 3 ΩR2​ = 4 Ω+−V1​20 VR3​5 ΩAR4​3 ΩBI1​I2​

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

V1 = 20 VR1 = 3 ΩR2 = 4 ΩR3 = 5 ΩR4 = 3 Ω
I2 = A
3.Medium
R1​ = 2 ΩIR1​R2​ = 5 Ω+−V1​6 VR3​10 ΩA+−V2​15 VI1​I2​

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

V1 = 6 VV2 = 15 VR1 = 2 ΩR2 = 5 ΩR3 = 10 Ω
IR1 = A
4.Medium
R1​ = 20 ΩR2​ = 2 Ω+−V1​30 VR3​15 ΩIR3​A+−V2​18 VI1​I2​

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

V1 = 30 VV2 = 18 VR1 = 20 ΩR2 = 2 ΩR3 = 15 Ω
IR3 = A
5.Hard
R1​ = 20 ΩR2​ = 3 ΩR3​ = 25 Ω+−V1​18 VR4​2 ΩAR5​30 ΩB+−V2​36 VI1​I2​I3​

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

V1 = 18 VV2 = 36 VR1 = 20 ΩR2 = 3 ΩR3 = 25 ΩR4 = 2 ΩR5 = 30 Ω
I3 = A
6.Hard
R1​ = 6 ΩR2​ = 30 ΩR3​ = 5 Ω+−V1​24 VR4​2 ΩAR5​20 Ω+−VR5​B+−V2​36 VI1​I2​I3​

Use mesh analysis to find the voltage VR5 across R5 with the polarity shown.

V1 = 24 VV2 = 36 VR1 = 6 ΩR2 = 30 ΩR3 = 5 ΩR4 = 2 ΩR5 = 20 Ω
VR5 = V

Answer key

  1. 1. VR1 = 14.79 V
  2. 2. I2 = 1.408 A
  3. 3. IR1 = −0.75 A
  4. 4. IR3 = 1.135 A
  5. 5. I3 = −1.187 A
  6. 6. VR5 = 26.23 V

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