Equivalent Resistance Between Terminals

[chunkytuna21]

What is the equivalent resistance of the circuit in Fig. P29 between terminals A and B? R1 = 5 , R2 = 5 , R3 = 5 and R4 = 1 . Note that the wires cross but do not make contact at the center.

V= IRe
IRe= IR1 +IR2
Series= Re= R1+R2
Parallel= 1/Re= 1/R1+R2
Re= R1R2/R1+R2

I am assuming all 4 resistors are parallel, right? So, I just plugged the values into the equation: 1/5+1/5+1/5+1/1= 1.6; 1/1.6= 0.625
This isn't the answer though. Where am I going wrong? I know they are not in series because I tried that already. Any help is greatly appreciated.

 

[gamer_x_]

post picture as a link, we still can't see the attachment. What I do in these cases is redraw the circuit to actually show group the series and parallel resistors, that way it's easier to see where you can simplify.

 

[tomcue]

Your approach is correct, but you have made a small error in your calculation. The equivalent resistance in this circuit is not 0.625, it is actually 1.25. Let's break down the steps to see where the error occurred:

1. First, we need to identify the resistors that are in parallel. In this circuit, R1, R2, and R3 are all in parallel, while R4 is in series with the other three resistors.

2. Next, we can use the formula for calculating equivalent resistance in parallel circuits: 1/Re = 1/R1 + 1/R2 + 1/R3

3. Plugging in the values, we get: 1/Re = 1/5 + 1/5 + 1/5 = 3/5

4. To find the equivalent resistance, we need to take the reciprocal of both sides: Re = 5/3 = 1.67

5. Now, we need to add the resistance of R4, which is in series with the other three resistors. So, the final equivalent resistance is: Re = 1.67 + 1 = 2.67 ohms.

So, the equivalent resistance between terminals A and B is 2.67 ohms. The error in your calculation occurred when you took the reciprocal of 1.6 instead of 1.67. I hope this helps clarify things for you.