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​ = 2 Ω+−VR1​R2​ = 4 Ω+−V1​20 VR3​10 ΩAR4​6 ΩBI1​I2​

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

V1 = 20 VR1 = 2 ΩR2 = 4 ΩR3 = 10 ΩR4 = 6 Ω
VR1 = V
2.Easy
R1​ = 6 ΩR2​ = 2 Ω+−V1​12 VR3​2 Ω+−VR3​AR4​3 ΩBI1​I2​

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

V1 = 12 VR1 = 6 ΩR2 = 2 ΩR3 = 2 ΩR4 = 3 Ω
VR3 = V
3.Medium
R1​ = 6 ΩR2​ = 4 Ω+−V1​24 VR3​6 ΩA+−V2​10 VI1​I2​

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

V1 = 24 VV2 = 10 VR1 = 6 ΩR2 = 4 ΩR3 = 6 Ω
I1 = A
4.Medium
R1​ = 10 ΩR2​ = 3 Ω+−VR2​+−V1​10 VR3​4 ΩA+−V2​12 VI1​I2​

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

V1 = 10 VV2 = 12 VR1 = 10 ΩR2 = 3 ΩR3 = 4 Ω
VR2 = V
5.Hard
R1​ = 12 ΩR2​ = 30 ΩR3​ = 20 Ω+−V1​24 VR4​20 ΩIR4​AR5​4 ΩB+−V2​18 VI1​I2​I3​

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

V1 = 24 VV2 = 18 VR1 = 12 ΩR2 = 30 ΩR3 = 20 ΩR4 = 20 ΩR5 = 4 Ω
IR4 = A
6.Hard
R1​ = 4 ΩR2​ = 2 ΩR3​ = 12 Ω+−V1​10 VR4​2 ΩAR5​20 Ω+−VR5​B+−V2​15 VI1​I2​I3​

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

V1 = 10 VV2 = 15 VR1 = 4 ΩR2 = 2 ΩR3 = 12 ΩR4 = 2 ΩR5 = 20 Ω
VR5 = V

Answer key

  1. 1. VR1 = 5.714 V
  2. 2. VR3 = 2.308 V
  3. 3. I1 = 2.143 A
  4. 4. VR2 = −4.683 V
  5. 5. IR4 = 0.6398 A
  6. 6. VR5 = 5.192 V

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