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Perhatikan rangkaian listrik berikut. Menurut hukum Kirchhoff, rangkaian listrik di atas dapat dinyatakan dalam sistem persamaan: ⎩⎨⎧​I1​−I2​−I3​=06−5I1​−10I3​=06−5I1​−3I2​=0​  Hitunglah kuat arus I1​, I2​ dan I3​

Pertanyaan

Perhatikan rangkaian listrik berikut.

Menurut hukum Kirchhoff, rangkaian listrik di atas dapat dinyatakan dalam sistem persamaan:

open curly brackets table attributes columnalign left end attributes row cell I subscript 1 minus I subscript 2 minus I subscript 3 equals 0 end cell row cell 6 minus 5 I subscript 1 minus 10 I subscript 3 equals 0 end cell row cell 6 minus 5 I subscript 1 minus 3 I subscript 2 equals 0 end cell end table close 

Hitunglah kuat arus I subscript 1 comma space I subscript 2 space dan space I subscript 3 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

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kuat arus Error converting from MathML to accessible text.I subscript 2 equals 0 comma 632 dan Error converting from MathML to accessible text. 

Pembahasan

Diketahui:

open curly brackets table attributes columnalign left end attributes row cell I subscript 1 minus I subscript 2 minus I subscript 3 equals 0 space...... space left parenthesis 1 right parenthesis end cell row cell 6 minus 5 I subscript 1 minus 10 I subscript 3 equals 0 space rightwards double arrow space 5 I subscript 1 plus 10 I subscript 3 equals 6 space... space left parenthesis 2 right parenthesis end cell row cell 6 minus 5 I subscript 1 minus 3 I subscript 2 equals 0 space rightwards double arrow space 5 I subscript 1 plus 3 I subscript 2 equals 6 space....... space left parenthesis 3 right parenthesis end cell end table close 

Eliminasi (1) dan (2), maka:

table row cell I subscript 1 minus I subscript 2 minus I subscript 3 equals 0 end cell cell open vertical bar cross times 10 close vertical bar end cell cell 10 I subscript 1 minus 10 I subscript 2 minus 10 I subscript 3 equals 0 end cell row cell 5 I subscript 1 plus 10 I subscript 3 equals 6 end cell cell open vertical bar cross times 1 close vertical bar end cell cell 5 I subscript 1 plus 10 I subscript 3 equals 6 space space plus end cell row blank blank cell 15 I subscript 1 minus 10 I subscript 2 equals 6 space... space left parenthesis 4 right parenthesis end cell end table

Eliminasi (3) dan (4), maka:

table row cell 5 I subscript 1 plus 3 I subscript 2 equals 6 end cell cell open vertical bar cross times 3 close vertical bar end cell cell 15 I subscript 1 plus 9 I subscript 2 equals 18 end cell row cell 15 I subscript 1 minus 10 I subscript 2 equals 6 end cell cell open vertical bar cross times 1 close vertical bar end cell cell 15 I subscript 1 minus 10 I subscript 2 equals 6 space space space minus end cell row blank blank cell 19 I subscript 2 equals 12 end cell row blank blank cell I subscript 2 equals 0 comma 632 end cell end table

Substitusi I subscript 2 equals 0 comma 632 ke salah satu persamaan yaitu 5 I subscript 1 plus 3 I subscript 2 equals 6, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 I subscript 1 plus 3 I subscript 2 end cell equals 6 row cell 5 I subscript 1 plus 3 left parenthesis 0 comma 632 right parenthesis end cell equals 6 row cell 5 I subscript 1 plus 1 comma 896 end cell equals 6 row cell 5 I subscript 1 end cell equals cell 6 minus 1 comma 896 end cell row cell 5 I subscript 1 end cell equals cell 4 comma 104 end cell row cell I subscript 1 end cell equals cell 0 comma 8208 end cell end table

 Substitusi I subscript 1 equals 0 comma 8208 ke persamaan space 5 I subscript 1 plus 10 I subscript 3 equals 6, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell space 5 I subscript 1 plus 10 I subscript 3 end cell equals 6 row cell 5 left parenthesis 0 comma 8208 right parenthesis plus 10 I subscript 3 end cell equals 6 row cell 4 comma 104 plus 10 I subscript 3 end cell equals 6 row cell 10 I subscript 3 end cell equals cell 6 minus 4 comma 104 end cell row cell 10 I subscript 3 end cell equals cell 1 comma 896 end cell row cell I subscript 3 end cell equals cell 0 comma 1896 end cell end table

Jadi, kuat arus Error converting from MathML to accessible text.I subscript 2 equals 0 comma 632 dan Error converting from MathML to accessible text. 

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