Total Resistance – How to Find Total Resistance of a Circuit

circuit analysisresistance

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?

Best Answer

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.

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