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​ = 8 ΩIR2​+−V1​12 VR3​6 ΩAR4​4 ΩBI1​I2​

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

V1 = 12 VR1 = 8 ΩR2 = 8 ΩR3 = 6 ΩR4 = 4 Ω
IR2 = A
2.Easy
R1​ = 8 ΩR2​ = 8 Ω+−V1​18 VR3​8 Ω+−VR3​AR4​10 ΩBI1​I2​

Use mesh analysis to find the voltage VR3 across R3 with the polarity shown.

V1 = 18 VR1 = 8 ΩR2 = 8 ΩR3 = 8 ΩR4 = 10 Ω
VR3 = V
3.Medium
R1​ = 5 Ω+−VR1​R2​ = 4 Ω+−V1​9 VR3​8 ΩA+−V2​18 VI1​I2​

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

V1 = 9 VV2 = 18 VR1 = 5 ΩR2 = 4 ΩR3 = 8 Ω
VR1 = V
4.Medium
R1​ = 4 ΩIR1​R2​ = 8 Ω+−V1​30 VR3​6 ΩA+−V2​30 VI1​I2​

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

V1 = 30 VV2 = 30 VR1 = 4 ΩR2 = 8 ΩR3 = 6 Ω
IR1 = A
5.Hard
R1​ = 30 ΩR2​ = 12 ΩR3​ = 10 Ω+−V1​12 VR4​2 ΩAR5​3 ΩB+−V2​9 VI1​I2​I3​

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

V1 = 12 VV2 = 9 VR1 = 30 ΩR2 = 12 ΩR3 = 10 ΩR4 = 2 ΩR5 = 3 Ω
I2 = A
6.Hard
R1​ = 12 ΩR2​ = 5 ΩR3​ = 20 Ω+−V1​5 VR4​20 ΩAR5​2 Ω+−VR5​B+−V2​9 VI1​I2​I3​

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

V1 = 5 VV2 = 9 VR1 = 12 ΩR2 = 5 ΩR3 = 20 ΩR4 = 20 ΩR5 = 2 Ω
VR5 = V

Answer key

  1. 1. IR2 = 0.3333 A
  2. 2. VR3 = 7.364 V
  3. 3. VR1 = −1.957 V
  4. 4. IR1 = 2.308 A
  5. 5. I2 = −0.082 A
  6. 6. VR5 = 1.111 V

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