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 ΩR2​ = 5 Ω+−V1​24 VR3​4 ΩAR4​12 Ω+−VR4​BI1​I2​

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

V1 = 24 VR1 = 4 ΩR2 = 5 ΩR3 = 4 ΩR4 = 12 Ω
VR4 = V
2.Easy
R1​ = 6 ΩR2​ = 8 Ω+−V1​20 VR3​6 ΩAR4​10 ΩBI1​I2​

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

V1 = 20 VR1 = 6 ΩR2 = 8 ΩR3 = 6 ΩR4 = 10 Ω
I1 = A
3.Medium
R1​ = 12 ΩIR1​R2​ = 2 Ω+−V1​10 VR3​10 ΩA+−V2​15 VI1​I2​

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

V1 = 10 VV2 = 15 VR1 = 12 ΩR2 = 2 ΩR3 = 10 Ω
IR1 = A
4.Medium
R1​ = 15 ΩR2​ = 2 Ω+−V1​15 VR3​5 ΩA+−V2​6 VI1​I2​

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

V1 = 15 VV2 = 6 VR1 = 15 ΩR2 = 2 ΩR3 = 5 Ω
I2 = A
5.Hard
R1​ = 4 Ω+−VR1​R2​ = 4 ΩR3​ = 30 Ω+−V1​30 VR4​2 ΩAR5​4 ΩB+−V2​9 VI1​I2​I3​

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

V1 = 30 VV2 = 9 VR1 = 4 ΩR2 = 4 ΩR3 = 30 ΩR4 = 2 ΩR5 = 4 Ω
VR1 = V
6.Hard
R1​ = 8 ΩR2​ = 20 Ω+−VR2​R3​ = 2 Ω+−V1​15 VR4​15 ΩAR5​30 ΩB+−V2​9 VI1​I2​I3​

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

V1 = 15 VV2 = 9 VR1 = 8 ΩR2 = 20 ΩR3 = 2 ΩR4 = 15 ΩR5 = 30 Ω
VR2 = V

Answer key

  1. 1. VR4 = 7.579 V
  2. 2. I1 = 1.905 A
  3. 3. IR1 = −0.1829 A
  4. 4. I2 = −0.3913 A
  5. 5. VR1 = 21.35 V
  6. 6. VR2 = 0.993 V

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