Pertanyaan

Diberikan gambar rangkaian star dan rangkaian delta seperti berikut. Jika diketahui R a = R 1 + R 2 + R 3 R 1 R 2 R b = R 1 + R 2 + R 3 R 2 R 3 R c = R 1 + R 2 + R 3 R 1 R 3 Maka bentuk persamaan R 3 yang tepat adalah ….

Diberikan gambar rangkaian star dan rangkaian delta seperti berikut.

Jika diketahui

$R_{a} = \frac{R _{1} R _{2}}{R _{1} + R _{2} + R _{3}} R_{b} = \frac{R _{2} R _{3}}{R _{1} + R _{2} + R _{3}} R_{c} = \frac{R _{1} R _{3}}{R _{1} + R _{2} + R _{3}}$

Maka bentuk persamaan R₃ yang tepat adalah ….

$begin mathsize 12px style R subscript 3 equals fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript a end fraction end style$
$begin mathsize 12px style R subscript 3 equals fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript b end fraction end style$
$begin mathsize 12px style R subscript 3 equals fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript c end fraction end style$
$begin mathsize 12px style R subscript 3 equals fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript a plus R subscript b plus R subscript c end fraction end style$
$begin mathsize 12px style R subscript 3 equals fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript a plus R subscript b end fraction end style$

M. Robo

Master Teacher

Jawaban terverifikasi

Pembahasan

Bandingkan R a dengan R b Bandingkan R b dengan R c Substitusi persamaan (2) ke persamaan (1) Substitusi persamaan (1) dan (3) ke bentuk R c Jadi, jawaban yangtepat adalah A.

Bandingkan R_adengan R_b

$begin mathsize 14px style R subscript a over R subscript b equals fraction numerator open parentheses begin display style fraction numerator R subscript 1 R subscript 2 over denominator R subscript 1 plus R subscript 2 plus R subscript 3 end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator R subscript 2 R subscript 3 over denominator R subscript 1 plus R subscript 2 plus R subscript 3 end fraction end style close parentheses end fraction R subscript a over R subscript b equals R subscript 1 over R subscript 3 R subscript 1 equals open parentheses R subscript a over R subscript b close parentheses R subscript 3 space... space... space... left parenthesis 1 right parenthesis end style$

Bandingkan R_bdengan R_c

$size 14px R subscript size 14px b over size 14px R subscript size 14px c size 14px equals fraction numerator begin mathsize 14px style begin display style left parenthesis fraction numerator R subscript 2 R subscript 3 over denominator R subscript 1 plus R subscript 2 plus R subscript 3 end fraction right parenthesis end style end style over denominator begin mathsize 14px style begin display style left parenthesis fraction numerator R subscript 1 R subscript 3 over denominator R subscript 1 plus R subscript 2 plus R subscript 3 end fraction right parenthesis end style end style end fraction size 14px R subscript size 14px b over size 14px R subscript size 14px c size 14px equals size 14px R subscript size 14px 2 over size 14px R subscript size 14px 1 size 14px R subscript size 14px 2 size 14px equals begin mathsize 14px style left parenthesis R subscript b over R subscript c right parenthesis end style size 14px R subscript size 14px 1 size 14px space size 14px. size 14px. size 14px. size 14px space size 14px. size 14px. size 14px. size 14px space size 14px. size 14px. size 14px. size 14px left parenthesis size 14px 2 size 14px right parenthesis$

Substitusi persamaan (2) ke persamaan (1)

Substitusi persamaan (1) dan (3) ke bentuk R_c

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell R subscript c end cell equals cell fraction numerator R subscript 3 open parentheses begin display style R subscript a over R subscript b end style left parenthesis R subscript 3 right parenthesis close parentheses over denominator open parentheses begin display style R subscript a over R subscript b end style R subscript 3 close parentheses plus open parentheses R subscript a over R subscript c R subscript 3 close parentheses plus R subscript 3 end fraction end cell row cell R subscript c end cell equals cell fraction numerator R subscript a over R subscript b left parenthesis R subscript 3 right parenthesis over denominator open parentheses R subscript a over R subscript b close parentheses plus open parentheses R subscript a over R subscript c close parentheses plus 1 end fraction end cell row cell R subscript c end cell equals cell fraction numerator open parentheses begin display style fraction numerator R subscript a R subscript 3 over denominator R subscript b end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript b R subscript c end fraction end style close parentheses end fraction end cell row cell R subscript c end cell equals cell fraction numerator open parentheses begin display style R subscript a R subscript 3 end style close parentheses over denominator open parentheses begin display style fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript c end fraction end style close parentheses end fraction end cell row cell R subscript c end cell equals cell fraction numerator R subscript a R subscript 3 R subscript c over denominator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c end fraction end cell row 1 equals cell fraction numerator R subscript a R subscript 3 over denominator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c end fraction end cell row cell R subscript a R subscript 3 end cell equals cell R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c end cell row cell R subscript 3 end cell equals cell fraction numerator R subscript a R subscript c plus R subscript a R subscript b plus R subscript b R subscript c over denominator R subscript a end fraction end cell end table end style$

Jadi, jawaban yangtepat adalah A.

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