CBSE Class 12 · 2006 · All India · Current ElectricityShort Answer

You are given

n

resistors, each of resistance

r

. They are first connected to get the minimum possible resistance and then connected differently to get the maximum possible resistance. Compute the ratio of the minimum to the maximum resistance so obtained.

Answer: $\frac{R _{m i n}}{R _{m a x}} = \frac{1}{n ^{2}}$ , i.e. $1 : n^{2}$ .

Solution

Minimum resistance is obtained with all

n

in parallel:

R_{m i n} = \frac{r}{n}

. Maximum is obtained with all

n

in series:

R_{m a x} = n r

. Hence

\frac{R _{m i n}}{R _{m a x}} = \frac{r / n}{n r} = \frac{1}{n ^{2}} .

CBSE Class 12 Board · 2006 · All India · Subjective

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