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​ = 8 Ω+−VR1​R2​ = 12 Ω+−V1​15 VR3​6 ΩAR4​6 ΩBI1​I2​

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

V1 = 15 VR1 = 8 ΩR2 = 12 ΩR3 = 6 ΩR4 = 6 Ω
VR1 = V
2.Easy
R1​ = 10 ΩR2​ = 6 Ω+−V1​15 VR3​3 ΩAR4​10 ΩBI1​I2​

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

V1 = 15 VR1 = 10 ΩR2 = 6 ΩR3 = 3 ΩR4 = 10 Ω
I1 = A
3.Medium
R1​ = 8 ΩR2​ = 5 ΩIR2​+−V1​6 VR3​12 ΩA+−V2​30 VI1​I2​

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

V1 = 6 VV2 = 30 VR1 = 8 ΩR2 = 5 ΩR3 = 12 Ω
IR2 = A
4.Medium
R1​ = 20 ΩR2​ = 4 Ω+−V1​24 VR3​5 ΩIR3​A+−V2​18 VI1​I2​

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

V1 = 24 VV2 = 18 VR1 = 20 ΩR2 = 4 ΩR3 = 5 Ω
IR3 = A
5.Hard
R1​ = 15 ΩR2​ = 30 ΩR3​ = 5 Ω+−V1​30 VR4​4 ΩIR4​AR5​30 ΩB+−V2​36 VI1​I2​I3​

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

V1 = 30 VV2 = 36 VR1 = 15 ΩR2 = 30 ΩR3 = 5 ΩR4 = 4 ΩR5 = 30 Ω
IR4 = A
6.Hard
R1​ = 20 ΩR2​ = 8 Ω+−VR2​R3​ = 5 Ω+−V1​15 VR4​10 ΩAR5​4 ΩB+−V2​5 VI1​I2​I3​

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

V1 = 15 VV2 = 5 VR1 = 20 ΩR2 = 8 ΩR3 = 5 ΩR4 = 10 ΩR5 = 4 Ω
VR2 = V

Answer key

  1. 1. VR1 = 9.6 V
  2. 2. I1 = 1.197 A
  3. 3. IR2 = −2.694 A
  4. 4. IR3 = 2.28 A
  5. 5. IR4 = 2.096 A
  6. 6. VR2 = 1.316 V

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