Question

In the circuit shown in fig. the heat produced in 5$\Omega$ resistor due to a current flowing in it is 10 cal /s. The heat produced in 4 $\Omega$ resistor is -

• A. 4 cal /s
• B. 1 cal /s
• C. 2 cal /s
• D. 3 cal /s

Answer 1

The correct option is C 2 cal /s

Drawing equivalent circuit diagram $4\Omega$ and $6\Omega$ are in series $\Rightarrow 10\Omega$ is equivalent

Taking current I in $10\Omega$ branch and accordingly $2I$ in $5\Omega$ branch for the voltage to remain same i.e., $I\times 10=2I\times 5$

Heat produced in $5\Omega$ resistor $=(2I{)}^{2}R$

per unit time

$10=4I^2\times 5$

$I^2=\frac{10}{4\times 5}$

$\Rightarrow I^2=\frac{1}{2}$

$I=0.7071$

Then,

Heat produced in $4\Omega$ resistor $=(I{)}^{2}R$

per unit time

Heat per unit time $=\frac{1}{2}\times 4=2$ cal/s.