Question

A heating coil has a resistance of $200\Omega $ .At what rate will heat be produced in it when a current of $2.5{\rm A}$ flows through it?

Answer 1

Hint: When current flows through a coil for a time then it will generate some amount of heat across the coil which also depends on the resistance of the coil. By using this concept of heat generation across the coil we can solve this above problem.

Complete step by step solution:
Heat is a form of energy that is transferred between systems or objects with different temperatures. Heat is typically measured in joules. Heat flow, or the rate at which heat is transferred between systems, has the same units as power $\left( {J{s^{ - 1}}} \right)$ .
The heating effect produced by an electric current, through a conductor of resistance R, for a time t, which is represented as follow,
$H = {I^2}Rt \cdot \cdot \cdot \cdot \left( 1 \right)$
Where, t=Time
H= Heat Produce
I= Current through the coil
R= Resistance of the coil
This equation $\left( 1 \right)$ is also known as the Joules Equation of electrical heating.
As given is the problem,
$R = 200\Omega $
The SI unit of resistance is Ohm.
$I = 2.5A$
The current SI unit is Ampere.
We need to calculate the Rate of heat produce,
By using equation $\left( 1 \right)$ , we get
$H = {I^2}Rt$
By rearranging the above equation we get,
$\dfrac{H}{t} = {I^2}R \cdot \cdot \cdot \cdot \left( 2 \right)$
In equation $\left( 2 \right)$
$\dfrac{H}{t} = $ Rate of heat produce
Rate of heat produced in the coil is also known as Power, where the SI unit is in $J{s^{ - 1}}$ .
Hence,
Rate of heat produce$ = {I^2}R$
Putting the given respective values as per the question, we get
Rate of heat produce$ = {\left( {2.5} \right)^2} \times \left( {200} \right)\,\,J{s^{ - 1}}$
$ \Rightarrow $ Rate of heat produce $ = 6.25 \times 200\,J{s^{ - 1}}$
$ \Rightarrow $Rate of heat produce$ = 1250\,J{s^{ - 1}}$
Therefore, the correct answer to this problem is $1250\,\,J{s^{ - 1}}$ .

Note:
Generally we do get to know what rate of heat means and try to calculate the amount of heat produced by the coil. But it is not the correct way as the rate of heat produced means power. And also in this problem time is not given.