When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 2.25 J2 then the value of R in Ω is.

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When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J₁. When the same batteries are connected in parallel across R, the rate is J₂. If J₁ = 2.25 J₂ then the value of R in Ω is.

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$\frac{J_{2}}{J_{1}} = {(\frac{I_{2}}{I_{1}})}_{}^{2} = \frac{1}{2 .25} \Rightarrow \frac{I_{2}}{I_{1}} = \frac{1}{1 .5}$

$I_{1} = \frac{2 E}{R + 2}$

$I_{2} = \frac{E}{R + \frac{1}{2}} = \frac{2 E}{2 R + 1}$

$\Rightarrow \frac{I_{2}}{I_{1}} = \frac{R + 2}{(2 R + 1)} \Rightarrow \frac{32}{23} = \frac{R + 2}{2 R + 1}$

14R + 2 = 3R + 6

R = 4

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