Question

A hot electric iron has a resistance of $80\Omega $ and is used on a $200V$ source. The electrical energy spent, if used for $2h$ is:
$\begin{align}
  & \text{A}\text{. }8000Wh \\
 & \text{B}\text{. 2}000Wh \\
 & \text{C}\text{. 1}000Wh \\
 & \text{D}\text{. 3}00Wh \\
\end{align}$

Answer 1

Hint: When an electric current flows through a liquid or solid device with finite conductivity, electric energy is converted into heat through resistive losses in the material. The heat which is produced by the flow of electric current in an electric wire is expressed in the unit of Joules. We will use the expression for the Joule’s heating effect to determine the energy spent in the circuit.

Formula used:
\[H=\left( \dfrac{{{V}^{2}}}{R} \right)t\]

Complete step by step answer:
When current flows through an electric circuit, the collision between the electrons and atoms of wire causes heat to be generated.
Joule heating, also called resistive heating, describes the process where the energy of an electric current is converted into heat as it flows through a resistance.
In particular, when an electric current flows through a solid or liquid material of finite conductivity, electric energy is converted into heat energy through resistive losses in the material. The heat is generated on the micro scale when the conduction electrons transfer energy to the conductor's atoms by way of collisions. The heat that is produced due to the flow of electric current within an electric wire is expressed in a unit of Joules.
The mathematical expression for Joule’s law:
$H={{I}^{2}}Rt$
Where,
$I$ is the current in the circuit
$R$ is the resistance
$t$ is the time
Or,
\[H=\left( \dfrac{{{V}^{2}}}{R} \right)t\]
Where,
$V$ is the potential difference
$R$ is the resistance
$t$ is the time
The amount of heat energy produced in a current carrying wire is proportional to the square of the amount of electric current that is flowing through the wire, while the electrical resistance of the wire and the time of current flowing through the circuit are constant.
$H\propto {{I}^{2}}$
Where,
$R$ and $t$ are constant
The amount of heat produced in the circuit or wire is proportional to the electrical resistance of the wire while the current in the wire and the time of current flowing are constant.
$H\propto R$
Where,
$I$ and $t$ are constant
The heat generated due to the flow of current is proportional to the time of current flowing, when the electrical resistance and the amount of current is constant.
$H\propto t$
Where,
$I$ and $R$ are constant
We are given that electric iron has a resistance of $80\Omega $ and is used on a $200V$ source for$2h$,
Voltage $V=200V$
Resistance, $R=800\Omega $
Time $T=2h$
Electrical energy spent will be,
$E=\left( \dfrac{{{V}^{2}}}{R} \right)t$
Putting values, we get,
$\begin{align}
  & E=\dfrac{{{\left( 200 \right)}^{2}}}{80}\times 2 \\
 & E=1000Wh \\
\end{align}$
The total electrical energy spent in the circuit will be $1000Wh$
Hence, the correct option is C.

Note:
Joule heating effect describes the process where the energy of an electric current is converted into heat as it flows through a resistance. Energy spent in the circuit is directly proportional to the amount of current in the circuit and inversely proportional to the resistance of the device. As long as the electric current is flowing, more energy will be spent in the circuit.