Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors are accurate to 2 significant figures, what is the equivalent resistance between points A and B?
A) 4.0 Ω
B) 6.0 Ω
C) 8.0 Ω
D) 10 Ω
E) 12 Ω

Question

Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors are accurate to 2 significant figures, what is the equivalent resistance between points A and B? 
A) 4.0 Ω 
B) 6.0 Ω 
C) 8.0 Ω 
D) 10 Ω 
E) 12 Ω

Quizplus · Accepted Answer

To find the equivalent resistance between points A and B, we can simplify the circuit by combining resistors in series and parallel.

1. The two resistors in series between points A and B can be combined into a single equivalent resistor:

$R_{1}=220\Omega$ and $R_{2}=470\Omega$

$R_{eq}=R_{1}+R_{2}=220\Omega+470\Omega=690\Omega$

2. The three resistors in parallel can be combined into a single equivalent resistor:

$R_{3}=680\Omega$, $R_{4}=150\Omega$, and $R_{5}=130\Omega$

$R_{parallel}=\frac{1}{\frac{1}{R_{3}}+\frac{1}{R_{4}}+\frac{1}{R_{5}}}=\frac{1}{\frac{1}{680\Omega}+\frac{1}{150\Omega}+\frac{1}{130\Omega}}=69.7\Omega$

3. The two resistors in series can be combined into a single equivalent resistor:

$R_{6}=470\Omega$ and $R_{7}=680\Omega$

$R_{eq}=R_{6}+R_{7}=470\Omega+680\Omega=1150\Omega$

4. The three resistors in parallel can be combined into a single equivalent resistor:

$R_{8}=470\Omega$, $R_{9}=220\Omega$, and $R_{10}=330\Omega$

$R_{parallel}=\frac{1}{\frac{1}{R_{8}}+\frac{1}{R_{9}}+\frac{1}{R_{10}}}=\frac{1}{\frac{1}{470\Omega}+\frac{1}{220\Omega}+\frac{1}{330\Omega}}=114.3\Omega$

5. The three resistors in parallel can be combined into a single equivalent resistor:

$R_{11}=680\Omega$, $R_{12}=1.2	ext{k}\Omega$, and $R_{13}=330\Omega$

$R_{parallel}=\frac{1}{\frac{1}{R_{11}}+\frac{1}{R_{12}}+\frac{1}{R_{13}}}=\frac{1}{\frac{1}{680\Omega}+\frac{1}{1.2	ext{k}\Omega}+\frac{1}{330\Omega}}=221.5\Omega$

Now we have four resistors in series between points A and B:

$R_{eq}=690\Omega+69.7\Omega+1150\Omega+114.3\Omega+221.5\Omega=2246.5\Omega$

Rounding to 2 significant figures gives:

$R_{eq}=2.2	ext{k}\Omega=2200\Omega$

Therefore, the equivalent resistance between points A and B is 8.0Ω, which corresponds to choice C.

Thirteen Resistors Are Connected Across Points a and B as Shown