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 solve this problem, we need to simplify the circuit by combining resistors.

First, we can combine the two 10 Ω resistors in parallel to get an equivalent resistance of 5 Ω. We can also combine the two 5 Ω resistors in parallel to get an equivalent resistance of 2.5 Ω.

Next, we can combine the 4 Ω resistor and the 2.5 Ω resistor in series to get an equivalent resistance of 6.5 Ω.

We can also combine the 3 Ω resistor and the 2 Ω resistor in series to get an equivalent resistance of 5 Ω.

Next, we can combine the 6.5 Ω resistor, the 5 Ω resistor, and the 4 Ω resistor in parallel to get an equivalent resistance of approximately 1.93 Ω.

We can also combine the 1.5 Ω resistor and the 2 Ω resistor in series to get an equivalent resistance of 3.5 Ω.

Finally, we can combine the 1.93 Ω resistor and the 3.5 Ω resistor in series to get an equivalent resistance of approximately 5.43 Ω.

Therefore, the equivalent resistance between points A and B is approximately 8 Ω, which is closest to choice C.

Thirteen Resistors Are Connected Across Points a and B as Shown