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How do I find the equivalent resistance between terminals A and F? The only idea I had was simplifying the parallel 300 and 60 resistors, but where to from there?

Circuit

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  • \$\begingroup\$ That's a good start. You might find a series combination to simplify next. If necessary, redraw each simplified circuit and post where you get stuck. \$\endgroup\$ – Brian Drummond Jan 16 '16 at 16:39
  • \$\begingroup\$ That's a start. Parallel the 300/60,series with the 50,parallel with the 150, and ignore the 200. \$\endgroup\$ – WhatRoughBeast Jan 16 '16 at 16:39
  • \$\begingroup\$ Does that mean there is no current flowing throught the 200? \$\endgroup\$ – Quant Jan 16 '16 at 16:42
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You can redraw it like this:

schematic

simulate this circuit – Schematic created using CircuitLab

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1, below, is the original problem.

In 2, the 300 and 60 ohm resistors in parallel resolve to an equivalent resistance of:

$$ Rt = \frac {300 \Omega \times 60\Omega}{360\Omega+60\Omega} = 50 \text{ ohms,}$$ morphed to RA lower down.

RA is in series with R4, for a total of 100 ohms, and that 100 ohms is in parallel with R3, as shown in 3 with the resistors rearranged for clarity.

The equivalent resistance of R3, R4, and RA, then, will be:

$$ Rt = \frac {(RA +R4) \times R3}{RA+R4+R3} = 60 \text{ ohms} $$

The total resistance from A to F, then, is the sum of the 60 ohms connected to A, the 200 ohms connected to F, and the 60 ohms in series between them.

enter image description here

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  • \$\begingroup\$ Thank you for the detailed answer! One thing that's confusing me with these problems is the order I'm solving the resistors. For example, I would've solved (2) this way: 50 and 50 in series give 100, which is parallel to the 150. This gives us 60 ohms. Finally, the equivalent resistance would be 60 + 60 + 200 = 320 ohms. I don't know if I'm wrong in my judgment, but my first reaction was this. How can these solutions not match? Thanks \$\endgroup\$ – Quant Jan 16 '16 at 18:32
  • \$\begingroup\$ @Quant you are correct, it is 320 Ohm. \$\endgroup\$ – Steve G Jan 16 '16 at 19:34
  • \$\begingroup\$ I apologize for the sloppy work. It is, indeed, 320 ohms. \$\endgroup\$ – EM Fields Jan 16 '16 at 20:06

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