In the circuit shown identical resistors R are connected in parallel (n > 1) and the combination is connected in series to another resistor R0. In the adjoining circuit n resistors of resistance R are all connected in series along with R0. The batteries in both circuits are identical and net power dissipated in the n resistors in both circuits is same. The ratio R0/R is

Engineering

Physics

Question

In the circuit shown identical resistors R are connected in parallel (n > 1) and the combination is connected in series to another resistor R₀. In the adjoining circuit n resistors of resistance R are all connected in series along with R₀. The batteries in both circuits are identical and net power dissipated in the n resistors in both circuits is same. The ratio R₀/R is

n²

1/n

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$p = {(\frac{E}{R_{0} + \frac{R}{m}})}^{2} \times \frac{R}{n} = {(\frac{E}{R_{0} + nR})}^{2} \times nR$
$\Rightarrow n^{2} = \frac{{(R_{0} + nR)}^{2}}{{(R_{0} + \frac{R}{n})}^{2}}$
$\Rightarrow {nR}_{0} + R = R_{0} + nR$
(n – 1)R₀ = (n –1)R
R₀= R.