Circuits...Total Resistance...?

Question

What I am trying to figure out is what single equivalent resistor could replace all of these resistors in this particular circuit. Since i can't draw it i will explain it to you. There is a pair of resistors in parallel ...5 and 9 ohms. Combining these brings about a pair in series... 2 ohms and the answer you got with combining the ones in parallel ( i got 2 + 3.2142857= 5.2142857) Now this single equivalent resistor is parallel to one...14 ohms. In doing this I got 12.22782 for the equivalent resistor to replace all of these, but it is wrong. Any ideas....Much thanks in advance

Answer 1

You got the first part right. But 5.214..... in parallel with anything has to be less than 5.214.....
It's Rt = 1/((1/R1) + (1/R2) + ...) so
Rt = 1/(1/5.214.....) + (1/14)) = 3.799.....

HTH ☺


Doug

Answer 2

Make a circuit diagram including all the resistors. Calculate the equivalent resistor of the first two resistors in parallel and draw a new diagram. Add any resistors in series and draw a new diagram, etc. That will make the process very clear until you can use shortcuts.

Answer 3

I cannot picture this with your description.

You say "Combining these brings about a pair in series.....).

What does that mean?

[R_t = Total Resistance]

For resistors in series you have:

R_t = R1 + R2 + R3 + ····


For resistors in parallel you have:

1/R_t = 1/R1 + 1/R2 + 1/R3 + ····

Apply this to each grouping in turn and you will eventually get to where you end up with one resistance. I know it's ahrd to describe these kinds of things without diagrams, but I'm sorry, I just don't understand the geometry of your curcuit.


:(

Answer 4

The answer I got was 3.8 ohms because the 5.21 ohm resistor paralleled with the 14 ohm gave me 73/19.21 which came to around 3.8 ohms