Question

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

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

Answer 1

Answer: (B)

$2$ cal/sec

$H=I^{2}Rt\to \left(1\right)$

Given:

$H=10caloriesR=5\Omega$

Current can be evaluated from equation $\left(1\right)$

$10=I^2\times 5\times t\frac{10}{5}=I^{2}t=2=(\frac{I}{2}{)}^2\times t=(\frac{2}{4})\to (2)$

Heat generated in $4\Omega$ resistance is

Let $H^1$

And we know that current is $\propto \frac{1}{R}$

Here in this branch $(4\Omega$ resistance is $10\Omega$ so current will be half of $5\Omega$ (branch)

$H=(\frac{I}{2}{)}^2\times 4\times t$ (t=constant in both cases)

$H=\left(\frac{2}{4}\right)\times 4\times t$ from equation $\to \left(2\right)$

$H=2cal/sec$