Jika 3 hambatan listrik yang besamya masing-masing 1 ohm, 2 ohm dan 3 ohm dirangkaikan, akan diperoleh 8 macam kombinasi. Hitunglah hambatan pengganti dari ke delapan kombinasi tersebut!

Pertanyaan

Jika 3 hambatan listrik yang besamya masing-masing 1 ohm, 2 ohm dan 3 ohm dirangkaikan, akan diperoleh 8 macam kombinasi. Hitunglah hambatan pengganti dari ke delapan kombinasi tersebut!

D. Wildatul

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Diketahui :

italic R subscript 1 equals 1 space capital omega italic R subscript 2 equals 2 space capital omega italic R subscript 3 equals 3 space capital omega 

 

Pembahasan :

3 buah hambatan yang dirangkai akan menghasilkan 8 kombinasi rangkaian seperti pada gambar berikut.

 

Hambatan pengganti pada setiap kombinasi

Kombinasi 1

table attributes columnalign right center left columnspacing 0px end attributes row cell italic R subscript italic s end cell equals cell italic R subscript 1 plus italic R subscript 2 plus italic R subscript 3 end cell row blank equals cell 1 plus 2 plus 3 end cell row blank equals cell 6 space capital omega end cell end table 

 

Kombinasi 2

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 1 plus 1 over italic R subscript 2 plus 1 over italic R subscript 3 end cell row cell 1 over italic R subscript italic p end cell equals cell 1 over 1 plus 1 half plus 1 third end cell row cell 1 over italic R subscript italic p end cell equals cell fraction numerator 6 plus 3 plus 2 over denominator 6 end fraction end cell row cell italic R subscript italic p end cell equals cell 6 over 11 space A end cell end table 

 

Kombinasi 3

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 2 plus 1 over italic R subscript 3 end cell row cell 1 over italic R subscript italic p end cell equals cell 1 half plus 1 third end cell row cell 1 over italic R subscript italic p end cell equals cell fraction numerator 3 plus 2 over denominator 6 end fraction end cell row cell italic R subscript italic p end cell equals cell 6 over 5 space capital omega space end cell row blank blank blank row cell italic R subscript italic s end cell equals cell italic R subscript 1 plus italic R subscript italic p end cell row blank equals cell 1 plus 6 over 5 end cell row blank equals cell 11 over 5 capital omega space end cell end table 

 

Kombinasi 4

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 1 plus 1 over italic R subscript 3 end cell row cell 1 over italic R subscript italic p end cell equals cell 1 over 1 plus 1 third end cell row cell 1 over italic R subscript italic p end cell equals cell fraction numerator 3 plus 1 over denominator 3 end fraction end cell row cell italic R subscript italic p end cell equals cell 3 over 4 space capital omega space end cell row blank blank blank row cell italic R subscript italic s end cell equals cell italic R subscript 2 plus italic R subscript italic p end cell row blank equals cell 2 plus 3 over 4 end cell row blank equals cell 11 over 4 capital omega space end cell end table 

 

Kombinasi 5

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 1 plus 1 over italic R subscript 2 end cell row cell 1 over italic R subscript italic p end cell equals cell 1 over 1 plus 1 half end cell row cell 1 over italic R subscript italic p end cell equals cell fraction numerator 2 plus 1 over denominator 2 end fraction end cell row cell italic R subscript italic p end cell equals cell 2 over 3 space capital omega space end cell row blank blank blank row cell italic R subscript italic s end cell equals cell italic R subscript 3 plus italic R subscript italic p end cell row blank equals cell 3 plus 2 over 3 end cell row blank equals cell 11 over 3 capital omega space end cell end table 

 

Kombinasi 6

table attributes columnalign right center left columnspacing 0px end attributes row cell italic R subscript italic s end cell equals cell italic R subscript 2 plus italic R subscript italic 3 end cell row blank equals cell 2 plus 3 end cell row blank equals cell 5 space capital omega end cell row blank blank blank row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 1 plus 1 over italic R subscript s end cell row cell 1 over italic R subscript italic p end cell equals cell 1 over 1 plus 1 fifth end cell row cell 1 over italic R subscript italic p end cell equals cell fraction numerator 5 plus 1 over denominator 5 end fraction end cell row cell italic R subscript italic p end cell equals cell 5 over 6 space capital omega space space end cell end table 

 

Kombinasi 7

table attributes columnalign right center left columnspacing 0px end attributes row cell italic R subscript italic s end cell equals cell italic R subscript 1 plus italic R subscript italic 3 end cell row blank equals cell 1 plus 3 end cell row blank equals cell 4 space capital omega end cell row blank blank blank row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 2 plus 1 over italic R subscript s end cell row cell 1 over italic R subscript italic p end cell equals cell 1 half plus 1 fourth end cell row cell 1 over italic R subscript italic p end cell equals cell fraction numerator 2 plus 1 over denominator 4 end fraction end cell row cell italic R subscript italic p end cell equals cell 4 over 3 space capital omega space space end cell end table 

 

Kombinasi 8

table attributes columnalign right center left columnspacing 0px end attributes row cell italic R subscript italic s end cell equals cell italic R subscript 1 plus italic R subscript italic 2 end cell row blank equals cell 1 plus 2 end cell row blank equals cell 3 space capital omega end cell row blank blank blank row cell 1 over italic R subscript italic p end cell equals cell 1 over italic R subscript 3 plus 1 over italic R subscript s end cell row cell 1 over italic R subscript italic p end cell equals cell 1 third plus 1 third end cell row cell 1 over italic R subscript italic p end cell equals cell 2 over 3 end cell row cell italic R subscript italic p end cell equals cell 3 over 2 space capital omega space space end cell end table 

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