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Resistance independent of cells ?

1 vote

At what value of Resistance $R_I$ in the circuit shown in figure will the total resistance between points A and B be independent of the number of cells ?

I didn't understand what does question mean by asking independent of number of cells ?
Rest I feel it's based on some infinite resistors like problem but don't get the last words.

asked Jan 13, 2018 in Physics Problems by physicsapproval (2,320 points)
The question is saying that the resistance $R_I$ is the same as $R_{AB}$. Treat the network as being infinitely long. Then the addition of an extra unit makes no difference.
Still I'm unable to feel practically what it wants to convey. What do you mean by extra unit ?
An extra unit is the repeating unit in the ladder network : a  vertical resistor $R$ followed by a horizontal resistor $2R$ to the right of it.

If the network is infinitely long then inserting such a unit in front of AB will make no difference to the total resistance. If you cut the network vertically just after any $2R$ resistor then everything to the right of the cut is again an infinitely long network made up of the same units. So the resistance to the right of the cut has exactly the same value as the resistance across AB.

So the resistor $R_I$ should be equivalet to an infinite ladder of the same units.
So is it that by cell the question means not the batteries but the 'repeating unit' of resistor?
And yes I have got your point :)
Yes, the question is talking about the number of repeating units.

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