In this circuit, when certain current flows, the heat produced in $5 \Omega$ is $4.05 \mathrm{~J}$ in a time t. The heat produced in $2 \Omega$ coil in the same time interval is

• A

  $2.02$
• B

  $5.76$
• C

  $1.44$
• Correct answer
  D

  $2.88$

Solution

Let, the current distribution is as shown, then by current divider rule,

$H_{1}=\frac{(6+9)}{(6+9)+5} I=\frac{3}{4} I$ Let $\mathrm{H}$ and $\mathrm{H}_{1}$ be heat produced in $2 \Omega$ and $5 \Omega$ resistors respectively in time t, then $$ \begin{gathered} \mathrm{H}=\mathrm{I}^{2}(2) \mathrm{t}=2 \mathrm{I}^{2} \mathrm{t} \\ \text { and } \mathrm{H}_{1}=\mathrm{I}_{1}^{2}(5) \mathrm{t}=\mathrm{II}_{1}^{2} \mathrm{t}=\frac{45}{16} \mathrm{I}^{2} \mathrm{t} \\ \therefore \quad \frac{\mathrm{H}}{\mathrm{H}_{\mathrm{I}}}=\frac{32}{45}=\frac{32}{45} \times 4.05 \mathrm{~J}=2.88 \mathrm{~J} \end{gathered} $$

Hence, the correct answer is option: 'D'.