# (science) (loop 2): 12V How many amperes are going through (I) 1,2, and 3 (loop 2): Vt=VR3+VR4

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valentin68 | College Teacher | (Level 3) Associate Educator

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To find the currents `I_1` , `I_2` and `I_3` one need to write the corresponding Kirchhoff laws for the voltages on the loops shown in the figure:

`V = I2*R3 +(I2+I3)*R4`

`V =(I1+I3)*R1 +I3*R5 +(I2+I3)*R4`

`V = (I1+I3)R1 +I1*R2`

And we obtain a system of equations in the unknown `I1, I2, I3`

`I1*(100+50) +I3*100 =12`

`I2*(40+25) +I3*25 =12`

`I1*100 +I2*25 +I3*(100+75+25) =12`

which is equivalent to

`150*I1 +100*I3=12`

`65*I2 +25*I3 =12`

`100*I1 +25*I2 +200*I3 =12`

Solving we get the values of currents

`I1 =402/4825 =0.0833 A =83.3 mA`

`I2 =36/193 =0.1865 A =186.5 mA`

`I3 =-24/4825 =-0.0050 A =-5 mA`

Check:

`100*0.0833 +25*0.1865 -200*0.005 =11.993 V`

Check OK!

Answer: The values of the currents I1, I2 and I3 are 83.3 mA, 186.5 mA and -5 mA

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