$N$ lamps of resistance $r,$ each are fed by a source of resistance $R$ . Let light be proportional to square of heat produced, then the most efficient way of arranging lamps is to place them in parallel rows each containing $n$ lamps, when $n$ is nearly equal to :

\sqrt{\frac{N R}{r}}

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\sqrt{\frac{N r}{R}}

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\sqrt{\frac{R}{N r}}

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\sqrt{\frac{r}{N R}}

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Solution

The correct option is A $\sqrt{\frac{N R}{r}}$
There will be $\frac{N}{n}$ branches each containing $n$ lamps.

Total resistance seen by the source = $R + \frac{n r}{N / n} = R + \frac{n^{2} r}{N}$

Total heat = $H = \frac{V^{2}}{R + \frac{n^{2} r}{N}}$

Light $\propto H^{2}$ (Given in question)

Therefore, for most efficient method, maximum heat/power will be transferred when
$\frac{n^{2} r}{N} = R \Rightarrow n = \sqrt{\frac{N R}{r}}$

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N lamps of resistance r, each are fed by a source of resistance R. Let light be proportional to square of heat produced, then the most efficient way of arranging lamps is to place them in parallel rows each containing n lamps, when n is nearly equal to :

The correct option is A √NRrThere will be Nn branches each containing n lamps.Total resistance seen by the source = R+nrN/n=R+n2rNTotal heat = H=V2R+n2rNLight ∝H2 (Given in question)Therefore, for most efficient method, maximum heat/power will be transferred when n2rN=R⇒n=√NRr

$N$ lamps of resistance $r,$ each are fed by a source of resistance $R$ . Let light be proportional to square of heat produced, then the most efficient way of arranging lamps is to place them in parallel rows each containing $n$ lamps, when $n$ is nearly equal to :