D. HUBUNGAN ANTARA RANGKAIAN RESISTOR
1. Hubungan Seri Hambatan
Pada rangkaian ini berlaku
|
I₁ = I₂
= I₃ = I
|
Dan
|
Ԑ = V₁ + V₂ + V₃
|
ket : Ԑ = Beda tegangan total
V₁ =
tegangan pada resistor 1
V₂ = tegangan pada resistor 2
V₃ = tegangan pada resistor 3
Karena
:
|
Ԑ = IRs
|
Dan
|
V₁ = I₁ R₁
; V₂ = I₂
R₂ ; V₃
= I₃ R₃
|
Maka hambatan total seri adalah:
|
Rs
= R₁ +R₂
+₃
|
Ket : Rs
= hambatan total rangkaian seri
2.
Hubungan
Paralel resistor
Pada rangkaian ini berlaku
|
Ԑ
= V₁ = V₂
= V₃
|
|
I = I₁ + I₂
+ I₃
|
Ket:
I = kuat arus induk
I₁ = kuat arus cabang 1
I₂ = kuat arus cabang 2
I₃ = kuat arus cabang 3
Karena:
|
Ԑ
I = ―
Rp
|
Didapatkan
|
1 =
1
+
1 + 1
Rp Rp Rp Rp
|
Rp : hambatan total rangkaian parallel
Contoh:
1.
Jawab : R₅ dengan R₆ = paralel
1/R₅₆ = 1/R₅ + 1/R₆
1/R₅₆ = 1/20 + 1/20 = 2/20
1/R₅₆ = 20/2 = 10
R₄ dan R₅₆ = Rangkaian seri
Rs₄₅₆ = 90 + 10
= 100
1/R₃₄₅₆
= 1/R₃ + 1/R₄₅₆
1/R₃₄₅₆
= 1/100 + 1/100 = 2/100
1/R₃₄₅₆
= 100/2 = 50
Rs
= R₂ + R₃₄₅₆
= 150 + 50
= 200
R/₁₂₃₄₅₆
= 1/R₁ + 1/₁₂₃₄₅₆
= 1/200 + 1/200 = 2/200
= 200/2 = 100
2.
R₃ dengan R₅ = rangkaian seri
Rs = R₃ + R₅
R₃₅
= 9 + 3
= 12
R₄ , R₆ , dengan R₇ = Rangkaian Seri
Rs
= R₄ + R₆ + R₇
R₄₆₇ = 7 + 9 + 8
= 24
R₂₃₄₅₆₇ = Rangkaian Paralel
R₂₃₄₅₆₇ = 1/R₂ + 1/R₃₅ + 1/R₄₆₇
1/Rp = 1/8 + 1/12 + 1/24
1/Rp = 3/24 + 2/24 + 1/24
= 6/24
Rp = 24/6 =4
Rs
= 4 + 4 + 2
= 10
3.
R = R₁ + R₂ + R₃
= 6 + 6
= 12
= R₆ + R₇
= 6 + 6
= 12
R₃₄ , R₆₇ , dan R₈
Rs = R₃₄ + R₆₇ + R₈
Rs = 12 + 12 + 6
Rs = 30
R₅ dengan Rs = Paralel
Rp = 1/R₅ + 1/Rs
Rp = 5/30 + 1/30 = 6/30
Rp = 1/6 + 1/30
Rp = 30/6 =
5
R₁ , R₂ dan Rp = rangkaian Seri
Rs = R₁ + R₂ + Rp
= 6 + 6 + 5
= 17
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