what would the kvl be if -330i1-470i2-860i2+9=0 and -6-12-560i3-860i2+9=0 and -330i1-470i1+560i3+12+6=0 and i2=i1+i3.find i1, i2, i3.

Solutions

Expert Solution

first equation given is ::

-330 i₁- 470 i₂- 860 i₂ + 9=0

-330 i₁ -1330 i₂ = -9 Eq-1

second equation given is ::

-6-12- 560 i₃- 860 i₂+ 9=0

-860 i₂ - 560 i₃ = 9 Eq-2

third equation given is ::

-330 i₁ - 470 i₁ + 560 i₃ +12 + 6=0

- 800 i₁ + 560 i₃ = -18 Eq-3

i₂ = i₁ + i₃

i₃ = i₂ - i₁ Eq-4

replacing i₃ in Eq-2 by (i₂ - i₁ ) , we get

-860 i₂ - 560 (i₂ - i₁) = 9

560 i₁ - 1420 i₂ = 9 Eq-5

Solving Eq-1 and Eq-5

-330 i₁ -1330 i₂ = -9 Eq-1

560 i₁ - 1420 i₂ = 9 Eq-5

i₁ = 20.4 x 10^-3 A

i₂ = 1.71 x 10^-3 A

we know that

i₃ = i₂ - i₁

i₃ = 1.71 x 10^-3 A - 20.4 x 10^-3 A

i₃ = -18.69 x 10^-3 A

genius_generous answered 1 year ago

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