(B) To obtain the minimum possible resistance,all $n$ resistors must be connected in parallel.The equivalent resistance in parallel is given by $R_{\t

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(B) To obtain the minimum possible resistance,all $n$ resistors must be connected in parallel.The equivalent resistance in parallel is given by $R_{\text{min}} = \frac{r}{n}$.To obtain the maximum possible resistance,all $n$ resistors must be connected in series.The equivalent resistance in series is given by $R_{\text{max}} = n \times r$.The ratio of the minimum resistance to the maximum resistance is $\frac{R_{\text{min}}}{R_{\text{max}}} = \frac{r/n}{nr} = \frac{r}{n^2 r} = \frac{1}{n^2}$.

Class 12 Physics Current Electricity Equivalent Resistance - Series and Parallel , Circuit

Easy

You are given $n$ resistors each of resistance $r$. They are first connected to get the minimum possible resistance. In the second case,they are again connected differently to get the maximum possible resistance. Calculate the ratio between minimum and maximum values of resistance so obtained.

GUJCET 2006 All GUJCET

A
$n^2$
B
$\frac{1}{n^2}$
C
$\frac{1}{n}$
D
$n$

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Equivalent Resistance - Series and Parallel , Circuit

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You are given $n$ resistors each of resistance $r$. They are first connected to get the minimum possible resistance. In the second case,they are again connected differently to get the maximum possible resistance. Calculate the ratio between minimum and maximum values of resistance so obtained.

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