Question

In the adjoining figure, if $10$ calorie heat is produced per second in $5\Omega$ resistor due to the flow of current through it, then the heat produced in $6\Omega$ resistor is

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

Answer 1

The correct option is C $3cal/s$

Given, heat produced per second in $5\Omega$ resistor
$=10cal/s=10\times 4.2J/s$
So, $\frac{V^2}{5}=10\times 4.2$
or $V=\sqrt{10\times 4.2\times 5}V=\sqrt{42\times 5}V$
Potential difference across $A$ and $B=\sqrt{42\times 5}$
So, current in $6\Omega$,
$I=\frac{\sqrt{42\times 5}}{10}ampere$
Hence, heat produced in it,
$H={\left(\frac{\sqrt{42\times 5}}{10}\right)}^2\times 6J/s$
$=\frac{6}{4.2}\times \frac{6}{4.2}=3cal/s$.