Question

The electrical energy dissipated in a resistor is given by H = _______
A) $V \times {I^2} \times t$
B) ${V^2} \times I \times t$
C) $V \times I \times t$
D) $(V/I) \times t$

Answer 1

Hint: Dissipation is a term, which is often used to define the ways in which energy is wasted. Energy dissipated is given by power multiplied by time, and the power dissipated in a resistor is the energy dissipated per time.

Complete step by step answer:
Energy dissipated is given by power multiplied by time.
Let, \[q\] is the charge and $V$ is the potential drop across the resistor. Now, if charge $q$ moves through a resistor, it loses potential energy $qV$. This energy goes into heat and gets dissipated. Energy is transferred and some of that energy is dissipated whenever there is a change in a system. Dissipation is a term, which is often used to define the ways in which energy is wasted.
So, the power dissipated in a resistor is the energy dissipated per time, which means if an amount of charge $\delta q$ moves through the resistor in a time $\delta t$, the power loss is $P = \dfrac{{\delta qV}}{{\delta t}} = IV$ (where $I$ and $V$ is the current through the resistor and the voltage drop across it respectively).
Now, The power dissipated in a resistor can be obtained by using Ohm's law as we know $P = VI$ (where $I$ and $V$ is the current through the resistor and the voltage drop across it respectively). So, energy dissipated is given by $p \times t = V \times I \times t$
$\therefore$ The correct option C

Note: Ohm’s law states that if temperature and other physical conditions remain constant, the current flowing through a conductor is directly proportional to the potential difference between its two ends.
If the current and the potential drop across the current carrying-conductor is $I$ and $V$ respectively, then according to Ohm’s law, $V \propto I$ or, $V = IR$ (Where, $R$ is the constant, termed as ‘resistance’ of the conductor).