In the circuit shown in figure, the heat produced in the 5 Ω resistor due to the current flowing through it is 10 cals/s. The heat generated in the 4 Ω resistor is

In the circuit shown in figure, the heat produced in the $5 Ω$ resistor due to the current flowing through it is 10 cals/s. The heat generated in the $4 Ω$ resistor is

A
1 cal/s
B
2 cal/s
C
3 cal/s
D
4 cal/s

Solution:

$\begin{array}{l} P_{5} = i_{5}^{2} R, P_{5} = (i_{5}^{2}) 5 \\ i_{4} = \frac{i_{5}}{2} \Rightarrow P_{4} {(\frac{i_{5}}{2})}^{2} \times 4 \\ \frac{P_{4}}{P_{5}} = \frac{1}{5} \Rightarrow P_{4} = \frac{P_{5}}{5}, P_{4} = \frac{10}{4} = 2 cal / s \end{array}$

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