Question

An electric heater has a rating of \[1100\,W - 220\,V\]. How much electrical energy (in \[kW - h\]) will it consume in \[4{\text{ }}hours\]? What is the resistance of its element?

Answer 1

Hint:Here, it has been stated that the electric heater possesses some specification regarding its power at particular voltage supplied to it, we have to calculate the electrical energy with definition. We must remember the basic definitions of power, electrical energy and resistance. So that we can be able to calculate the required terms.

Complete step by step answer:
Now, according to the given condition we know that the electric heater has a rating of \[1100W - 220V\].
I\[Power,P = 1100W\] and \[Voltage,V = 220V\]
Now, we know that the power is defined as the product of voltage and the current across the conductor. And mathematically it is given by:
\[P = VI\] ; \[P\] is power, \[V\] is voltage and \[I\] is current through that circuit.
It can also be written as:
\[P = \dfrac{{{V^2}}}{R}\]..........…. \[\left( {\because I = \dfrac{V}{R}{\text{; R - resistance}}} \right)\]

From the given condition we will place values in above equation and find resistance in the given conductor as:
\[ \Rightarrow 1100 = \dfrac{{{{(220)}^2}}}{R}\]
\[ \Rightarrow R = 44\Omega \].............…. \[(1) \\ \]
Now for electrical energy we have,
Energy consumed is equivalent to the power supplied for the specific time in the circuit.
Therefore, \[{\text{Energy consumed = Power }} \times {\text{ Time}}\]
\[ \Rightarrow {\text{Energy consumed = 1100W}} \times {\text{4 hours}} \\ \]
But we need electrical energy in terms of \[kW - h\] , so the above equation can be written as:
\[ \Rightarrow {\text{Energy consumed = 1}}{\text{.1kW}} \times {\text{4 hours}}\]
\[ \therefore {\text{Energy consumed = 4}}{\text{.4kW - h}}\]

Hence the electrical energy consumed by the electric heater is obtained on calculating is \[4.4kW - h\] and the resistance is \[44\Omega \].

Note: Here, we should understand the concept that the power is related to voltage and resistance and use the definition accordingly, also the electrical energy is also the outcome of the similar relation. Hence we must remember the definitions and carefully do all the calculations here.