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When two identical batteries of internal resistance 1 \Omega each are connected in series across a resistor R, the rate of heat produced in R is \mathrm{J_1}. When the same batteries are connected I parallel across R, the rate is \mathrm{J_2}. If \mathrm{J_1=2.25 J_2} then the value of R in \Omega is

Option: 1

4


Option: 2

6


Option: 3

4.8


Option: 4

5.16


Answers (1)

best_answer

\begin{aligned} &\mathrm{ In ~series~ i=\frac{2 E}{2+R} }\\ &\mathrm{ \therefore \quad J_1=i^2 R=\left(\frac{2 E}{2+R}\right)^2 \cdot R }\\ &\mathrm{ \text{In parallel}}\\ \mathrm{i} &\mathrm{ =\frac{E}{0.5+R} }\\ \mathrm{J}_2 &\mathrm{ =i^2 R=\left(\frac{E}{0.5+R}\right)^2 \cdot R }\\ \mathrm{\frac{J_1}{J_2}} &\mathrm{ =2.25=\frac{4(0.5+R)^2}{(2+R)^2}}\\ &\mathrm{ \text{Solving we get, } R=4 \Omega}\\ \end{aligned}

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