Question

In the circuit shown in the figure, the heat produced in the $5$ ohm resistor due to the current flowing through it is $10$ calories per second. The heat generated in the $4$ ohm resistor is :

• A. $1$ calorie/sec
• B. $2$ calories/sec
• C. $3$ calories/sec
• D. $4$ calories/sec

Answer 1

Answer: (B)

$2$ calories/sec

Heat produced in resistance is given by,
$P=i^2\times R$
In parallel combination of resistance, current is inversely proportional to the resistance.
Therefore current through the upper branch will be half of the current flowing through the lower one.
For lower branch,
$10=i^2\times 5$
$i^2=2$
Therefore heat produced in upper 4 ohm resistance will be,
$P=(i/2{)}^2\times 4$
$P=2$ calories per sec.