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The Examples of High School Physics Problems and Solutions : Resistances in Series-Parallel (Grade 10)  and  how to find total resistance of 12 identic resistors that forming a cube.

Problem 1
Given three resistors shown below,



Find the total resistance of A-B!

Solution
The three resistances are connected in series, so the total resistance is equal to the sum of the resistances of A-B:

R_T = 2 + 3 + 6 = 11 Ohm

Problem 2
Find the total resistance for three resistors below!

Solution
The three resistances are connected in parallel so using the parallel formula :

Problem 3
Ten resistors, each having a resistance of 10 Ω , are arranged in series-parallel combinations shown below.



Find the total resistance!

Solution
R₂₃, the sum of R₂ and R₃ (series) :



R₄₆, the sum of R₄, R₅ and R₆ (series) :



R₇₁₀, the sum of R₇ , R₈ , R₉ and R₁₀(series) :



Using parallel formula for R₁, R₂₃, R₄₆ and R₇₁₀ give us R_AB:

1/R_AB = 1/10 + 1/20 + 1/30 + 1/40

1/R_AB = 12/120 + 6/120 + 4/120 + 3/120

Invert:

R_AB = 120 / 25 = 4,8 Ohm

Problem 4
Ten resistors, each having a resistance of 120 Ω, are arranged below.



Find the total resistance!

Solution
Using parallel formula for:
R₂ and R₃. The result is R₂₃ = 60 Ω
R₄ , R₅ and R₆. The result is R₄₆ = 40 Ω
R₇ , R₈ , R₉ and R₁₀ . The result is R₇₁₀ = 30 Ω
Series for R₁ , R₂₃ , R₄₆ dan R₇₁₀. The result is R_total = R_AB
R_AB = 120 + 60 + 40 + 30 = 250 Ω

Problem 5
Find the total resistance of eight resistors below:
R₁ = 10 Ω
R₂ = 2 Ω
R₃ = 3 Ω
R₄ = 17 Ω
R₅ = 20 Ω
R₆ = 20 Ω
R₇ = 8 Ω
R₈ = 10 Ω




Solution
→ Series for R₃ and R₄ → R₃₄
R₃₄ = R₃ + R₄ = 3 + 17 = 20 Ω
→ Parallel for R₅ and R₃₄ → R₃₅
R₃₅ = 10 Ω
→ Series for R₂, R₃₅ and R₇ → R₂₇
R₂₇ = 2 + 10 + 8 = 20 Ω
→ Parallel for R₂₇ and R₆ → R₂₇₆
R₂₇₆ = 10 Ω
→ Series for R₁ , R₂₇₆ and R₈ → R_AB or R_total

R_AB = 10 + 10 + 10 = 30 Ω

Problem 6
8 resistors, each having a resistance of 10 Ω, are arranged below!



Find the total resistance!

Solution
There will be no currents flow along R₂ and R₄ , so we could ignore them.
→ Series for R₅ and R₆ :
R₅₆ = 20 Ω
→ Series for R₇ and R₈ :
R₇₈ = 20 Ω
→ Parallel for R₅₆ and R₇₈ :
R₅₈ = 10 Ω
→ Series for R₁ , R₅₈ and R₃ to find R_PQ = R_total :

R_PQ = 10 + 10 + 10 = 30 Ω

and then, how to find total resistance of 12 identic resistors that forming a cube .

Problem 7
12 identic resistors are arranged and form a cube shown below.



Each resistor has 18 Ohm of resistance. Find the total resistance between P and Q!

Solution
Using the shortcut for this problem
R_total = ⁵/₆ R
R_total = ⁵/₆ (18) = 15 Ohm

Try This!
12 identic resistors are arranged and form a cube shown below.



Each resistor has 36 Ohm of resistance. Find the total resistance between P and Q!