Question

In the circuit shown in figure, the heat produced in the $5\Omega$ resistor due to the current flowing through it is $10\text{calories per second}$. The heat generated in the $4\Omega$ , resistor is

• A. $1\text{calorie/sec}$
• B. $2\text{calories/sec}$
• C. $3\text{calories/sec}$
• D. $4\text{calories/sec}$

Answer 1

The correct option is B $2\text{calories/sec}$

Heat produced in a resistor is, $H=i^{2}RT$
Given heat produced in $5\Omega$ resistor is
Here, $\frac{H_s}{t}=I_5^2{R}_5=10\text{cal}$
Current flowing through $5\Omega$ resistance is
$\Rightarrow I_5=\sqrt{\frac{10}{5}}=\sqrt{2}$

Voltage across resistor $5\Omega$ is $V_5=I_5{R}_5=\sqrt{2}\times 5=5\sqrt{2}\text{V}$

As resistors $(4\Omega ,6\Omega )$ and $5\Omega$ are in parallel, so potential across $(4\Omega ,6\Omega )$ is equal to $V_5$.

As resistors $4\Omega \text{and}6\Omega$ are in series so current through each resistor

$I_4=I_6=\frac{V_5}{4+6}=\frac{5\sqrt{2}}{4+6}=\frac{\sqrt{2}}{2}$.

Heat produced in resistor $4\Omega$ per sec is $I_4^2{R}_4={\left(\frac{\sqrt{2}}{2}\right)}^2\times \left(4\right)=2\text{cal}$