Question

An electric heater of resistance $8\Omega $ draws $15A$ from the service mains in $2$ hours. Calculate the rate at which heat is developed in the heater.

Answer 1

Hint
In the given question, we have been provided with the value of the resistance of the electric heater, the current it draws from the service mains and the time for which it operates, and we have been asked to find the rate at which heat is developed in the heater. Since heat is a form of energy, we have been asked the rate at which energy is consumed by the heater, which is analogous to the power of the heater.
$\Rightarrow P={{I}^{2}}R$

Complete step by step answer
We have been given that,
The current drawn by the electric heater $(I)=15A$
The resistance of the filament of the electric heater $(R)=8\Omega $
As discussed in the hint section, we know that any electric appliance when operates for a given period of time consumes some electrical energy; when we talk in terms of the rate at which the energy is consumed by an appliance, we are referring to the appliance’s power
The electric heater consumes energy from the circuit and this manifests in the form of heat energy obtained from its filament, so the rate of production of the heat energy can be said to be the power of the heater
We know the expression for the power of the circuit as $(P)={{I}^{2}}R$
Substituting the values in the above expression, we have-
$\Rightarrow P={{(15)}^{2}}\times 8$
$\Rightarrow P=225\times 8=1800W $

Note
If in the given question, we were also asked to find the total heat energy produced by the heater, we could multiply the obtained power of the heater with the time for which it is operated and find the total energy produced; as we know that the energy taken by any appliance is the product of its power rating and the time of operation.
But in this case, we did not need the time of operation; the examiner has set a trap for you, hence you are advised to only use the values you need and not worry about any other values that might be given in the question.