Determine the values of I_1, I_2, and I_3 that satisfy the following three equat

Question

Determine the values of I_1, I_2, and I_3 that satisfy the following three equations. -1.18 I_1 + I_2 + I_3 = 5.15, and -3.08 I_1 + I_2 = 0, and 1.50 I_1 + 1.50 I_3 = 0. I_1 = 276 (a) Your response differs from the correct answer by more than 10%. Double check (b) I_2 = 16.63 Your response is within 10% of the correct value. This may be due to roundoff error, or intermediate results to at least four-digit accuracy to minimize roundoff error. A I_3 = -5.15 Your response is within 10% of the correct value. This may be due to roundoff error, or intermediate results to at least four-digit accuracy to minimize roundoff error. A

Explanation / Answer

-1.18 I1 + I2 + I3 = 5.15

-3.08I1 + I2 = 0

1.5I1 + 1.5I3 = 0

from second eqn we get

I1 = 0.325 I2

from third eqn we get

I3 = -I1 = -0.325 I2

putting these values in eqn 1 we get

-1.18(0.325 I2) + I2 + (-0.325 I2) = 5.15

-0.384 I2 + I2 - 0.325 I2 = 5.15

(1 - 0.709)I2 = 5.15

I2 = 17.698 A

I1 = 0.325 I2 = 0.325 x 17.698 = 5.752 A

I3 = -0.325 I2 = -0.325 x 17.698 = -5.752 A

Hence, I1 = 5.752 ; I2 = 17.698 ; I3 = -5.752

check

-1.18 x 5.752 + 17.698 - 5.752 = 5.15

5.15 = 5.15

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