In the circuit shown in figure, the heat produced in $5\, ohm $ resistance is $10\, cal / sec$ . The heat produced in $4$ resistance is ................ $cal /sec$
IIT 1981, Medium
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$\frac{{{i_1}}}{{{i_2}}} = \frac{{{R_2}}}{{{R_1}}} = \frac{{10}}{5} = \frac{2}{1}$
Also heat produced per sec i.e. $\frac{H}{t} = P = {i^2}R$
Also heat produced per sec i.e. $\frac{H}{t} = P = {i^2}R$
$\frac{{{P_5}}}{{{P_4}}} = {\left( {\frac{{{i_1}}}{{{i_2}}}} \right)^2} \times \frac{5}{4} = {\left( {\frac{2}{1}} \right)^2} \times \frac{5}{4} = \frac{5}{1}$ $ \Rightarrow $ ${P_4} = \frac{{10}}{5} = 2\,cal/s$
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