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circuit

I want to find the total resistance between A and B. This is a HOTS mcq, which has the following options:

  • A: 45\$\Omega\$
  • B: 15\$\Omega\$
  • C: 5\$\Omega\$
  • D: 22.5\$\Omega\$

A book says that the answer is 5\$\Omega\$ as R1, R2 and R3 are parallel. But I cannot understand how can they be parallel? Our science teacher said that R1, R2 and R3 are in a series, so he said that total resistance R=45\$\Omega\$. The book that says that the answer is 5\$\Omega\$, does not have the method to find it out.

I tried that:

  1. All are in series :- 45\$\Omega\$

  2. 15\$\Omega\$ is parallel with 15+15+15\$\Omega\$ and with one more 15\$\Omega\$, which would turn into : 45/7\$\Omega\$, which is not possible.

  3. R3 is parallel with R1 and R2, as well as in a series with R2. R1 is parallel with R2 and R3, as well as in a series with R2 and R3. But then I cannot determine the method to get the answer.

So I am confused between 5\$\Omega\$ and 45\$\Omega\$. I think as the book says, the answer must be 5\$\Omega\$, but what is the method?

MarkU
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Ravishankar Joshi
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    The first step in these types of problems is always to redraw the circuit in a way that isn't nonsensical. – Matt Young Feb 20 '14 at 03:15
  • The book is correct. My professor explained it pretty well like this. Two things are in *parallel* when they both connect to the same nodes. Sounds simple, but that's all it is! Look at the left resistor, it connects node A with node B through the bottom short. The middle resistor connects node A and B through both shorts, and the right resistor connects A and B with the top short. – krb686 Feb 20 '14 at 03:20
  • Another way to think of it is current essentially always takes the path(s) of least resistance proportionally, right? So if you follow each path, you'll see there are 3 ways of traveling from A to B, each going through just 1 resistor. Current will NEVER travel through more than 1, since there is always an easier path. – krb686 Feb 20 '14 at 03:25

3 Answers3

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schematic

simulate this circuit – Schematic created using CircuitLab

Try redrawing the circuit with the 'A' connections in a bar at the top and the 'B' connections in a bar at the bottom (or use left/right).

They've deliberately made it confusing.

If you're redrawing, here's a set of guidelines that Olin wrote up:

Rules and guidelines for drawing good schematics

Community
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Spehro Pefhany
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Yes, R1, R2 & R3 are parallel to each other & hence, resultant resistance is 5 ohms. While finding equivalent resistance between any two points, imagine that you're travelling from one point to the other. Let's consider here that we're travelling from A to B.

One end of R2 is short-circuited to A & other end is short-circuited to B. Same is the case for R1 & R3.

That's why they fall parallel to each other & total resistance is 5 ohms.

yuvi
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the book is pretty correct as the circuit is like this:

schematic

simulate this circuit – Schematic created using CircuitLab This circuit would be in series if there were no wires shorting the circuit and then net resistance would be 15 ohm.

manav.tix
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  • While your explanation may be correct, your diagram doesn't match the original. His has 3 x 15R while yours has 3 x 5R. – brhans Dec 29 '15 at 14:47
  • yeah you are right i just forgot resistances were of 15ohm however that will have no effect on concept that i have used in the circuit. thanks for correction brhans – manav.tix Dec 29 '15 at 18:51