Question

In the circuit shown in the figure, the heat produced in the $5\Omega$ resistor due to a current flowing in it, is $10$ calories per second. The heat produced in the $4\Omega$ resistor is?

• A. $1$ cal $s^{-1}$
• B. $2$ cal $s^{-1}$
• C. $3$ cal $s^{-1}$
• D. $4$ cal $s^{-1}$

Answer 1

The correct option is B $2$ cal $s^{-1}$

$\frac{i_1}{i_2}=\frac{R_2}{R_1}=\frac{10}{5}=\frac{2}{1}$

Heat produced: $\frac{H}{t}=P=i^{2}R$

$\frac{P_5}{P_4}={\left(\frac{i_1}{i_2}\right)}^2\times \frac{5}{4}={\left(\frac{2}{1}\right)}^2\times \frac{5}{4}=\frac{5}{1}=P_4=\frac{10}{5}=2cal/s$