First slide

combination of resistance

Question

n resistances, 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

Easy

A

n²R
B

R/n²
C

R/n
D

nR

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
$\begin{array}{l} R^{'} = r + r + . .... + n times = nr \\ ∴ R^{'} = n (nR) = n^{2} R \end{array}$

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