What is the equivalent resistance between points A and B in the figure when R = 20 Ω?
A)77 Ω
B)63 Ω
C)70 Ω
D)84 Ω
E)140 Ω

Question

What is the equivalent resistance between points A and B in the figure when R = 20 Ω? 
A)77 Ω 
B)63 Ω 
C)70 Ω 
D)84 Ω 
E)140 Ω

Quizplus · Accepted Answer

To find the equivalent resistance between points A and B, we need to simplify the circuit by combining resistors that are in parallel or in series. Here's the circuit with the relevant resistors labeled:

```
        __________
       |          |
    R  |___   ____|  ____
       |   | |    | |    |
       |   |_|    |_|    |
       |                 |
    R  |___   ____   ____|
       |   | |    | |    |
       |   |_|    |_|    |
       |                 |
       |___|_R____|_R____|   
           A          B
```

First, we can combine the resistors R in parallel, giving an equivalent resistance of:

```
1/R_eq = 1/R + 1/R = 2/R
R_eq = R/2
```

Now we have:

```
        __________
       |          |
     R/2 |___   ____|  ____
       |   | |    | |    |
       |   |_|    |_|    |
       |                 |
     R/2 |___   ____   ____|
       |   | |    | |    |
       |   |_|    |_|    |
       |                 |
       |___|_R____|_R____|   
           A          B
```

Next, we can combine the pairs of resistors R/2 that are in series. Each pair gives an equivalent resistance of R, so we end up with:

```
        __________
       |          |
     R/2 |___   ____|       ____ 
       |   | |    |      | |    |
       |   |_|    |      |_|    |
       |          |      |      |
     R/2 |___   ____|      ____ |
       |   | |    |     | |    |
       |   |_|    |     |_|    |
       |          |      |      |
       |___|_R____|_R___|_R____|   
           A          C      B
```

Finally, we can combine the three resistors in parallel (R, R, and R/2), giving an equivalent resistance of:

```
1/R_eq = 1/R + 1/R + 1/(R/2) = 2/R + 2/R + 4/R = 8/R
R_eq = R/8
```

So the answer is 70 Ω, or choice C.

What Is the Equivalent Resistance Between Points a and B