Which among the following is an expression for energy?

Question

Examoogle · Accepted Answer

$\frac{V^2 t}{R}$

Explanation: Electrical energy is defined as the product of electrical power and the time duration for which the power is consumed. By applying Ohm's Law ($V = IR$), the power formula $P = VI$ can be substituted into the energy expression $E = P 	imes t = (\frac{V^2}{R})t$, resulting in the expression for energy as $E = \frac{V^2 t}{R}$.

Working Principle: Energy consumption in a resistive load occurs when current flows through a potential difference over time. Since $P = VI$ and $I = \frac{V}{R}$, substituting $I$ gives $P = V(\frac{V}{R}) = \frac{V^2}{R}$. Integrating this power over time $t$ yields the total work done or energy dissipated as heat: $E = \int P dt = \frac{V^2}{R} 	imes t$.

Key Formulas: $E = P 	imes t$ — Energy defined as Power times time; $E = \frac{V^2}{R} 	imes t$ — Energy in terms of Voltage, Resistance, and time

Key Points: Energy is the capacity to do work, measured in Joules (J) or Watt-seconds.; For purely resistive circuits, electrical energy is converted entirely into heat.; The expression $\frac{V^2 t}{R}$ is derived from Joule's Law of heating.

Advantages: Provides a direct calculation based on system voltage and load resistance.; Useful for sizing heating elements in industrial applications.

Disadvantages: Assumes constant resistance and constant voltage, which may vary in real power systems.; Does not account for non-ohmic (non-linear) devices like semiconductors.

Applications: Design of electric heaters and irons.; Energy consumption analysis in residential and industrial circuits.

Additional Info: Unit of Energy: 1 Joule = 1 Watt-second.. Option A ($V^2It$) is dimensionally incorrect (Units: $V^3/R 	imes t$). Option B ($V^2Rt$) is dimensionally incorrect (Units: $V^2R 	imes t$). Option D is incorrect as it uses $t^2$.

Answer: C is correct — The expression for electrical energy derived from Ohm's Law and the definition of power is $E = \frac{V^2 t}{R}$.

Exam Tip: Always verify dimensional consistency in electrical formulas; energy must always have the dimensions of Power × Time ($[M L^2 T^{-2}]$).

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