The heat generated in 5$\Omega$ resistor due to current flowing through it is 10 cal per sec. The heat generated in 4$\Omega$ resistor (in cal/sec) is _________

Resistance in upper branch is 10$\Omega$ and in lower branch is 5$\Omega$. Thus, if current in lower branch is i, current in upper branch is (i/2).

$\begin{array}{l}\text{ Now }{H}_4=(i/2{)}^2(4)\\ H_5=i^2\left(5\right)\\ \frac{H_4}{H_5}=\frac{1}{5}\\ \text{ or }{H}_4=\frac{H_5}{5}=\frac{10}{5}=2\mathrm{cal}/\sec \end{array}$