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 that are in series and parallel. 
Starting from the left side of the circuit, we can combine R1 and R2 in parallel:

R1||R2 = (R1*R2)/(R1+R2) = (6 * 4)/(6+4) = 2.4 Ω

Then, we can combine this parallel combination with R3 in series:

R1||R2 + R3 = 2.4 + 3 = 5.4 Ω

Continuing in this way, we can simplify the circuit as shown:

simplified circuit

Now we can combine the resistors in the middle of the circuit (R9, R10, R11) in parallel:

R9||R10||R11 = (R9*R10*R11)/(R9*R10 + R9*R11 + R10*R11) = (2 * 1 * 5)/(2*1 + 2*5 + 1*5) = 0.714 Ω

We can then combine this parallel combination with R8 in series:

R8 + R9||R10||R11 = 7 + 0.714 = 7.714 Ω

Finally, we can combine this with the parallel combination of R4, R5, R6, and R7:

(7 + R4||R5||R6||R7) || (R1||R2 + R3) = (7 + 1.111) || (5.4) = 8.03 Ω

So the equivalent resistance between points A and B is 8.0 Ω.

Thirteen Resistors Are Connected Across Points a and B as Shown