Exam

JIPMER

Year

2005

Subject

Physics

Chapter

Current Electricity

JIPMER 2005 · Physics · Current Electricity

When a certain current is passed in the circuit as shown in figure,...

When a certain current is passed in the circuit as shown in figure, 10 kcal of heat is produced in $5 \Omega$ resistance. How much heat is produced in $4 \Omega$ resistance?

Step-by-step solution

Heat produced in $5 \Omega=10 \mathrm{kcal}$ Now from the relation. $H_1=i_1^2 R_1 t or i_1^2=\frac{H_1}{R_1 t} or \quad i_1^2=\frac{H_1}{5 t}$ ...(1) Again, $5 \times i_1=10 \times i_2$ or $i_2=\frac{i_1}{2}$
Now heat produced in $4 \Omega$ resistance is $$\begin{aligned} H_2 & =i_2^2 R_2 t \\ i_2^2 & =\frac{H_2}{R_2 t}\end{aligned}$$ or $\quad \frac{i_1^2}{4}=\frac{H_2}{4 t} or i_1^2=\frac{H_2}{t}$ ...(2) From eqs. (1) and (2) $$\begin{aligned} \frac{H_2}{t} & =\frac{H_1}{5 t} \\ \text{ or } \quad H_2 & =\frac{H_1}{5}=\frac{10}{2}=2 \mathrm{kcal}\end{aligned}$$