> Q. Resistances n, each of r ohm, when connected in parallel give an equivalent resistance of R ohm. If these resistances were connected in series, the combination would have a resistance in ohms, equal to – LIVE ANSWER TODAY

Q. Resistances n, each of r ohm, when connected in parallel give an equivalent resistance of R ohm. If these resistances were connected in series, the combination would have a resistance in ohms, equal to

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Resistances n, each of r ohm, when connected in parallel give an equivalent resistance of R ohm. If these resistances were connected in series, the combination would have a resistance in ohms, equal to

Solution:

Equivalent resistance of n resistances each of r ohm in parallel is given by

$ frac{1}{R}=frac{1}{r}+frac{1}{r}+…..+n,times=frac{n}{r} $

So, $ r=nR $

When these resistances are connected in series, effective resistance is

$ R=r+r+……+ntext{ }times=nr $

$ therefore $ $ R=n(nR)={{n}^{2}}R $

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