Question

Calculate the heat produced in calorie when a current of $0.1\;A$ is passed through a wire of resistance $41.8\Omega $ for $5$ minutes.

Answer 1

Hint: In order to solve this question we must know the joule's law which states that,” when an electric current passes through a conductor, heat H is produced, which is directly proportional to the resistance R of the conductor, the time t for which the current flows, and square of the magnitude of current I. So from this equation we will initially convert the time in S.I unit to get the value of heat produced in joule and then finally by using relation between joule and calorie will get heat produced in calorie.

Complete step by step answer:
As we know according to the question the heat $\left( H \right)$ produced in wire due to current flow. So, According to Joules law the heat produced in a wire is given by,
$H={{I}^{2}}Rt$ ……………………$\left( 1 \right)$
Here, $I$ is current flowing through the wire, $R$ is the resistance and $t$ is time in seconds.
Now data given in the question is,
$I=0.1A$
$\Rightarrow R=41.8\Omega $
$\Rightarrow t=5\min $,
Now initially will convert time in S.I units which is seconds,
$t=5\times 60=300\sec $

Now in order to obtain the value of heat $\left( H \right)$ produced will substitute the value of $I$ , $R$ and $t$ in the equation $\left( 1 \right)$.
$H={{\left( 0.1 \right)}^{2}}\times 41.8\times 300=125.4J$
Hence heat produced in Joule is $125.4\;J$ .
As we know we want our final answer in calorie so by using relation between joules and calorie, which is given by,
$1\,calorie=4.184\,joule$ ,
So , $125.4\;J$ amount of heat produced in calorie is,
$H=\dfrac{125.4}{4.184} \\
\therefore H=29.9cal.\cong 30\,calorie$

Hence the heat produced in calorie is $30\;calorie$.

Note: Sir James Prescott Joule formulated Joules law which establishes the relation between voltage, current, time and resistance and the most important thing to note in this type of question is in which unit we are asked the value of heat produced, many of times we forgot to convert joule to calorie and another important conversion is of time, it must be converted to its S.I unit (second) otherwise we will not get our correct answer in joule which leads to incorrect final answer.