# Physics Learning Center

## Resistances Problems and Solutions

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:

RT = 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 RAB:

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

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

Invert:

RAB = 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 Rtotal = RAB
RAB = 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 → RAB or Rtotal

RAB = 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 RPQ = Rtotal :

RPQ = 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
Rtotal = 5/6 R
Rtotal = 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!

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