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 ΩR2​ = 5 Ω+−V1​6 VR3​8 ΩAR4​6 Ω+−VR4​BI1​I2​

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

V1 = 6 VR1 = 8 ΩR2 = 5 ΩR3 = 8 ΩR4 = 6 Ω
VR4 = V
2.Easy
R1​ = 3 ΩR2​ = 10 Ω+−V1​18 VR3​4 ΩAR4​10 ΩBI1​I2​

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

V1 = 18 VR1 = 3 ΩR2 = 10 ΩR3 = 4 ΩR4 = 10 Ω
I1 = A
3.Medium
R1​ = 2 ΩIR1​R2​ = 5 Ω+−V1​15 VR3​6 ΩA+−V2​9 VI1​I2​

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

V1 = 15 VV2 = 9 VR1 = 2 ΩR2 = 5 ΩR3 = 6 Ω
IR1 = A
4.Medium
R1​ = 8 ΩR2​ = 10 Ω+−V1​10 VR3​20 ΩA+−V2​30 VI1​I2​

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

V1 = 10 VV2 = 30 VR1 = 8 ΩR2 = 10 ΩR3 = 20 Ω
I2 = A
5.Hard
R1​ = 15 ΩR2​ = 5 ΩR3​ = 30 Ω+−V1​12 VR4​5 ΩAR5​4 ΩB+−V2​36 VI1​I2​I3​

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

V1 = 12 VV2 = 36 VR1 = 15 ΩR2 = 5 ΩR3 = 30 ΩR4 = 5 ΩR5 = 4 Ω
I3 = A
6.Hard
R1​ = 12 ΩR2​ = 5 Ω+−VR2​R3​ = 15 Ω+−V1​15 VR4​4 ΩAR5​6 ΩB+−V2​12 VI1​I2​I3​

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

V1 = 15 VV2 = 12 VR1 = 12 ΩR2 = 5 ΩR3 = 15 ΩR4 = 4 ΩR5 = 6 Ω
VR2 = V

Answer key

  1. 1. VR4 = 1.2 V
  2. 2. I1 = 2.842 A
  3. 3. IR1 = 2.135 A
  4. 4. I2 = −1.455 A
  5. 5. I3 = −1.071 A
  6. 6. VR2 = 0.1308 V

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